Pittner, Ludwig.
Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups [electronic resource] / by Ludwig Pittner. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1996. - XII, 469 pp. online resource. - Lecture Notes in Physics Monographs, 39 0940-7677 ; . - Lecture Notes in Physics Monographs, 39 .
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.
9783540478010
10.1007/978-3-540-47801-0 doi
Physics.
Quantum theory.
Mathematical physics.
Quantum computing.
Statistical physics.
Thermodynamics.
Physics.
Mathematical Methods in Physics.
Numerical and Computational Methods.
Quantum Physics.
Quantum Computing, Information and Physics.
Thermodynamics.
Statistical Physics.
QC5.53
530.15
Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups [electronic resource] / by Ludwig Pittner. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1996. - XII, 469 pp. online resource. - Lecture Notes in Physics Monographs, 39 0940-7677 ; . - Lecture Notes in Physics Monographs, 39 .
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.
9783540478010
10.1007/978-3-540-47801-0 doi
Physics.
Quantum theory.
Mathematical physics.
Quantum computing.
Statistical physics.
Thermodynamics.
Physics.
Mathematical Methods in Physics.
Numerical and Computational Methods.
Quantum Physics.
Quantum Computing, Information and Physics.
Thermodynamics.
Statistical Physics.
QC5.53
530.15