Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups
Pittner, Ludwig.
Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups [electronic resource] / by Ludwig Pittner. - XII, 469 p. 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
Mathematical physics.
Quantum theory.
Thermodynamics.
Mathematical Methods in Physics.
Numerical and Computational Physics, Simulation.
Quantum Physics.
Quantum Information Technology, Spintronics.
Thermodynamics.
Complex Systems.
QC5.53
530.15
Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups [electronic resource] / by Ludwig Pittner. - XII, 469 p. 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
Mathematical physics.
Quantum theory.
Thermodynamics.
Mathematical Methods in Physics.
Numerical and Computational Physics, Simulation.
Quantum Physics.
Quantum Information Technology, Spintronics.
Thermodynamics.
Complex Systems.
QC5.53
530.15