Home >> Seminar 

Quasi Lie algebras and Homalgebra structures
Sergei Silvestrov教授(瑞典Mälardalen大学应用数学系)
Monday, January 1st, 2018, 9:30 AM 华东师范大学 

曹锡华数学论坛
报告人简介：
瑞典Mälardalen大学应用数学系教授、Scientific leader for Mathematics and Applied Mathematics Research Environment (MAM)
报告内容简介：
In this talk, an introductory overview will be presented of some recent developments on the subject of Homalgebra, with focus on quasi Lie algebras, quasiHom Lie algebras, HomLie algebras and related Homalgebra structures. These objects appear for example when discretizing the differential calculus. Quasi Lie algebras encompass in a natural way the Lie algebras, Lie superalgebras, color Lie algebras, HomLie algebras, qLie algebras (proposed by Prof. N.H. Hu) and various algebras of discrete and twisted vector fields arising for example in connection to algebras of twisted discretized derivations, Ore extension algebras, qdeformed vertex operators structures and qdeferential calculus, multiparameter deformations of associative and nonassociative algebras, oneparameter and multiparameter deformations of infinitedimensional Lie algebras of Witt and Virasoro type some of which appear in the context of conformal field theory, string theory and deformed vertex models, multiparameter families of quadratic and almost quadratic algebras that include for special choices of parameters algebras appearing in noncommutative algebraic geometry, universal enveloping algebras of Lie algebras, Lie superalgebras and color Lie algebras and their deformations. Common unifying feature for all these algebras is appearance of some twisted generalizations of Jacoby identities providing new structures of interest for investigation from the side of associative algebras, nonassociative algebras, generalizations of Hopf algebras, noncommutative differential calculi beyond usual differential calculus and generalized quasiLie algebra central extensions and Homalgebra formal deformations and cohomology. Also in the talk, I will describe some related nary Homalgebra generalizations of Nambu algebras, associative algebras and Lie algebras.
主持人：胡乃红 教授
主办单位：数学系 科技处



