Carrell, James B.
Overview
Works:  43 works in 149 publications in 3 languages and 1,696 library holdings 

Genres:  Conference papers and proceedings Textbooks 
Roles:  Author, Editor, Contributor 
Classifications:  QA564, 512.944 
Publication Timeline
.
Most widely held works by
James B Carrell
Group actions and vector fields : proceedings of a PolishNorth American seminar held at the University of British Columbia,
January 15February 15, 1981 by
James B Carrell(
Book
)
27 editions published in 1982 in English and German and held by 558 WorldCat member libraries worldwide
27 editions published in 1982 in English and German and held by 558 WorldCat member libraries worldwide
Invariant theory, old and new by
Jean Dieudonné(
Book
)
13 editions published between 1970 and 1971 in English and held by 415 WorldCat member libraries worldwide
13 editions published between 1970 and 1971 in English and held by 415 WorldCat member libraries worldwide
Proceedings of the 1984 Vancouver conference in algebraic geometry, held July 212, 1984 by
Vancouver, British Columbia> Conference in Algebraic Geometry. <1984(
Book
)
14 editions published between 1984 and 1986 in English and held by 192 WorldCat member libraries worldwide
14 editions published between 1984 and 1986 in English and held by 192 WorldCat member libraries worldwide
Groups, matrices, and vector spaces : a group theoretic approach to linear algebra by
James B Carrell(
)
9 editions published between 2013 and 2017 in English and held by 168 WorldCat member libraries worldwide
This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a yearlong course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable
9 editions published between 2013 and 2017 in English and held by 168 WorldCat member libraries worldwide
This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a yearlong course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable
Topics in the theory of algebraic groups by
James B Carrell(
Book
)
9 editions published in 1982 in English and held by 168 WorldCat member libraries worldwide
9 editions published in 1982 in English and held by 168 WorldCat member libraries worldwide
Algebraic quotients by
Andrzej BiałynickiBirula(
)
14 editions published between 1993 and 2011 in English and held by 94 WorldCat member libraries worldwide
This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. BialynickiBirula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirtyfive years
14 editions published between 1993 and 2011 in English and held by 94 WorldCat member libraries worldwide
This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. BialynickiBirula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirtyfive years
Invariant theory and algebraic transformation groups(
Book
)
14 editions published in 2008 in English and held by 17 WorldCat member libraries worldwide
14 editions published in 2008 in English and held by 17 WorldCat member libraries worldwide
A group theoretic approach to abstract linear algebra by
James B Carrell(
Book
)
1 edition published in 2013 in English and held by 11 WorldCat member libraries worldwide
1 edition published in 2013 in English and held by 11 WorldCat member libraries worldwide
Invariant theory and algebraic transformation groups. Homogeneous spaces and equivariant embeddings(
Book
)
3 editions published in 2011 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 2011 in English and held by 5 WorldCat member libraries worldwide
Group Actions and Vector Fields by
James B Carrell(
)
2 editions published between 1982 and 2008 in English and held by 5 WorldCat member libraries worldwide
2 editions published between 1982 and 2008 in English and held by 5 WorldCat member libraries worldwide
Geometričeskaja teorija invariantov Ž. D'ëdonne; Dž. Kerrol; D. Mamford. Per. s angl. A.N. Paršina by
Jean Dieudonné(
Book
)
1 edition published in 1974 in Russian and held by 4 WorldCat member libraries worldwide
1 edition published in 1974 in Russian and held by 4 WorldCat member libraries worldwide
Invariant theory and algebraic transformation groups. Algebraic transformation groups and algebraic varieties : proceedings
of the conference Interesting algebraic varieties arising in algebraic transformation group theory, held at the Erwin Schrödinger
Institute, Vienna, October 2226, 2001(
Book
)
2 editions published in 2004 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2004 in English and held by 4 WorldCat member libraries worldwide
Invariant theory and algebraic transformation groups. Linear algebraic monoids(
Book
)
2 editions published in 2005 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2005 in English and held by 4 WorldCat member libraries worldwide
Invariant theory and algebraic transformation groups. Projective duality and homogenous spaces(
Book
)
2 editions published in 2005 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2005 in English and held by 4 WorldCat member libraries worldwide
Invariant theory, old and new [by] Jean A. Dieudonné [and] James B. Carrell by
Jean Dieudonné(
Book
)
1 edition published in 1971 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1971 in English and held by 4 WorldCat member libraries worldwide
Invariant theory and algebraic transformation groups. Multiplicative invariant theory(
Book
)
2 editions published in 2005 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2005 in English and held by 4 WorldCat member libraries worldwide
Invariant theory and algebraic transformation groups. Algebraic theory of locally nilpotent derivations(
Book
)
2 editions published in 2006 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 4 WorldCat member libraries worldwide
Topics in the Theory of Algebraic Groups by
James B Carrell(
)
1 edition published in 1983 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1983 in English and held by 3 WorldCat member libraries worldwide
The cohomology ring of a smooth manifold by
James B Carrell(
)
2 editions published in 1967 in English and held by 3 WorldCat member libraries worldwide
C.B. Allendorfer and J. Eells, Jr. have used pairs of singular differential forms to describe a cohomology theory alpha *(X, A) for any smooth paracompact manifold. This theory strengthens the de Rham theory since the coefficient group A may be taken to be any subring of the reals. Their main result is that alpha *(X, A) is canonically isomorphic to the Cech cohomology module H(X, A) of X with coefficients in A. The purpose of this paper is to describe a natural cup product for alpha *(X, A) so that alpha *(X, A) becomes a ring canonically isomorphic with the Cech cohomology ring H(X, A). (Author)
2 editions published in 1967 in English and held by 3 WorldCat member libraries worldwide
C.B. Allendorfer and J. Eells, Jr. have used pairs of singular differential forms to describe a cohomology theory alpha *(X, A) for any smooth paracompact manifold. This theory strengthens the de Rham theory since the coefficient group A may be taken to be any subring of the reals. Their main result is that alpha *(X, A) is canonically isomorphic to the Cech cohomology module H(X, A) of X with coefficients in A. The purpose of this paper is to describe a natural cup product for alpha *(X, A) so that alpha *(X, A) becomes a ring canonically isomorphic with the Cech cohomology ring H(X, A). (Author)
Proceedings of the 1984 Vancouver Conference in Algebraic Geometry : held July 212, 1984 by
Vancouver, British Columbia) Conference in Algebraic Geometry (1984(
Book
)
1 edition published in 1990 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1990 in English and held by 3 WorldCat member libraries worldwide
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Related Identities
 Dieudonné, Jean 19061992 Author Contributor
 Russell, P. (Peter) 1939 Editor
 Geramita, A. V. Editor
 University of British Columbia Other
 Natural Sciences and Engineering Research Council Canada Other
 BiałynickiBirula, Andrzej Author Editor
 McGovern, William M.
 Popov, Vladimir L. Editor
 Renner, Lex E.
 Derksen, Harm
Useful Links
Associated Subjects
Algebra Algebraic varieties Algebras, Linear Commutative algebra Commutative rings Geometry, Algebraic Global differential geometry Group actions (Mathematics) Group theory Homology theory Invariants Lie algebras Lie groups Linear algebraic groups Mathematical physics Mathematics Quotient rings Topological groups Torsion theory (Algebra) Vector fields
Covers
Alternative Names
Baldwin Carrell James
Carrell, J.
Carrell, J. B.
Carrell, J. B. 1940
Carrell, J. B. (James B.)
Carrell, James 1940
James B. Carrell Mathematiker
James Baldwin Carrell Amerikaans wiskundige
James Baldwin Carrell amerikansk matematikar
James Baldwin Carrell amerikansk matematiker
Kèrrol, Dž.
Kerrol, Dž. 1940
Керрол, Дж..
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