0000000000281690

AUTHOR

Murray Gerstenhaber

showing 3 related works from this author

Cohomology and Deformation of Leibniz Pairs

1995

Cohomology and deformation theories are developed for Poisson algebras starting with the more general concept of a Leibniz pair, namely of an associative algebra $A$ together with a Lie algebra $L$ mapped into the derivations of $A$. A bicomplex (with both Hochschild and Chevalley-Eilenberg cohomologies) is essential.

Pure mathematicsMathematics::Rings and AlgebrasStatistical and Nonlinear PhysicsDeformation (meteorology)Poisson distributionMathematics::Algebraic TopologyCohomologysymbols.namesakeMathematics::K-Theory and HomologyLie algebraAssociative algebraMathematics - Quantum AlgebrasymbolsFOS: MathematicsQuantum Algebra (math.QA)Mathematical PhysicsMathematics
researchProduct

The hidden group structure of Quantum Groups:strong duality,rigidity and preferred deformations

1994

International audience

[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT][MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT]ComputingMilieux_MISCELLANEOUS[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]
researchProduct

The hidden group structure of quantum groups: strong duality, rigidity and preferred deformations

1994

A notion of well-behaved Hopf algebra is introduced; reflexivity (for strong duality) between Hopf algebras of Drinfeld-type and their duals, algebras of coefficients of compact semi-simple groups, is proved. A hidden classical group structure is clearly indicated for all generic models of quantum groups. Moyal-product-like deformations are naturally found for all FRT-models on coefficients andC∞-functions. Strong rigidity (H bi 2 ={0}) under deformations in the category of bialgebras is proved and consequences are deduced.

Classical groupPure mathematicsQuantum groupDeformation theoryLie groupStatistical and Nonlinear PhysicsHopf algebra17B37Algebra81R50Compact groupMathematics::Quantum AlgebraStrong dualityDual polyhedron16W30Mathematical PhysicsMathematics
researchProduct