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Graduate Studies in Mathematics Ser.: Classical Groups and Geometric Algebra by American Mathem American Mathem (2001, Hardcover)
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About this product
Product Identifiers
PublisherAmerican Mathematical Society
ISBN-100821820192
ISBN-139780821820193
eBay Product ID (ePID)1979111
Product Key Features
Number of Pages169 Pages
LanguageEnglish
Publication NameClassical Groups and Geometric Algebra
SubjectGroup Theory, Geometry / Algebraic
Publication Year2001
TypeTextbook
AuthorAmerican Mathem American Mathem
Subject AreaMathematics
SeriesGraduate Studies in Mathematics Ser.
FormatHardcover
Dimensions
Item Height0.6 in
Item Weight19.3 Oz
Item Length10.3 in
Item Width7.4 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2001-046251
Dewey Edition21
Series Volume Number39
IllustratedYes
Dewey Decimal512/.2
Table Of ContentPermutation actions; The basic linear groups; Bilinear forms; Symplectic groups; Symmetric forms and quadratic forms; Orthogonal geometry (char $F\not= 2$); Orthogonal groups (char $F \not= 2$), I; $O(V)$, $V$ Euclidean; Clifford algebras (char $F \not = 2$); Orthogonal groups (char $F \not = 2$), II; Hermitian forms and unitary spaces; Unitary groups; Orthogonal geometry (char $F = 2$); Clifford algebras (char $F = 2$); Orthogonal groups (char $F = 2$); Further developments; Bibliography; List of notation; Index.
Synopsis'Classical groups', named so by Hermann Weyl, are groups of matrices or quotients of matrix groups by small normal subgroups. Thus the story begins, as Weyl suggested, with 'Her All-embracing Majesty', the general linear group $GL_n(V)$ of all invertible linear transformations of a vector space $V$ over a field $F$. All further groups discussed are either subgroups of $GL_n(V)$ or closely related quotient groups. Most of the classical groups consist of invertible linear transformations that respect a bilinear form having some geometric significance, e.g., a quadratic form, a symplectic form, etc. Accordingly, the author develops the required geometric notions, albeit from an algebraic point of view, as the end results should apply to vector spaces over more-or-less arbitrary fields, finite or infinite. The classical groups have proved to be important in a wide variety of venues, ranging from physics to geometry and far beyond.In recent years, they have played a prominent role in the classification of the finite simple groups. This text provides a single source for the basic facts about the classical groups and also includes the required geometrical background information from the first principles. It is intended for graduate students who have completed standard courses in linear algebra and abstract algebra. The author, L. C. Grove, is a well-known expert who has published extensively in the subject area., Classical groups, named so by Hermann Weyl, are groups of matrices or quotients of matrix groups by small normal subgroups. Thus the story begins, as Weyl suggested, with the general linear group GLULn(V) of all invertible linear transformations of a vector space V over a field F. All further groups discussed are either subgroups of GLULn(V) or closely related quotient groups. Most of the classical groups consist of invertible linear transformations that respect a bilinear form having some geometric significance, for example, a quadratic form, a symplectic form, and so forth., ''Classical groups'', named so by Hermann Weyl, are groups of matrices or quotients of matrix groups by small normal subgroups. Thus the story begins, as Weyl suggested, with ''Her All-embracing Majesty'', the general linear group $GL n(V)$ of all invertible linear transformations of a vector space $V$ over a field $F$. All further groups discussed are either subgroups of $GL n(V)$ or closely related quotient groups. Most of the classical groups consist of invertible linear transformations that respect a bilinear form having some geometric significance, e.g., a quadratic form, a symplectic form, etc. Accordingly, the author develops the required geometric notions, albeit from an algebraic point of view, as the end results should apply to vector spaces over more-or-less arbitrary fields, finite or infinite. The classical groups have proved to be important in a wide variety of venues, ranging from physics to geometry and far beyond. In recent years, they have played a prominent role in the classification of the finite simple groups. This text provides a single source for the basic facts about the classical groups and also includes the required geometrical background information from the first principles. It is intended for graduate students who have completed standard courses in linear algebra and abstract algebra. The author, L. C. Grove, is a well-known expert who has published extensively in the subject area., Intended for graduate students who have completed standard courses in linear algebra and abstract algebra, this title provides a single source for the basic facts about the classical groups and also includes the required geometrical background information from the first principles.
LC Classification NumberQA174.2.G78 2001
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