Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups. 1st ed. 1996

種類:

電子ブック

責任表示:

by Ludwig Pittner

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1996

著者名:

• Pittner, Ludwig.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Physics Monographs ; 39

ISBN:

9783540478010 [3540478019]    

注記:

Lie Algebras -- Lie Superalgebras -- Coalgebras and Z2-Graded Hopf Algebras -- Formal Power Series with Homogeneous Relations -- Z2-Graded Lie-Cartan Pairs -- Real Lie-Hopf Superalgebras -- Universal Differential Envelope -- Quantum Groups -- Categorial Viewpoint.
Quantum groups and quantum algebras as well as non-commutative differential geometry are important in mathematics. They are also considered useful tools for model building in statistical and quantum physics. This book, addressing scientists and postgraduates, contains a detailed and rather complete presentation of the algebraic framework. Introductory chapters deal with background material such as Lie and Hopf superalgebras, Lie super-bialgebras, or formal power series. A more general approach to differential forms, and a systematic treatment of cyclic and Hochschild cohomologies within their universal differential envelopes are developed. Quantum groups and quantum algebras are treated extensively. Great care was taken to present a reliable collection of formulae and to unify the notation, making this volume a useful work of reference for mathematicians and mathematical physicists.

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