报告题目 (Title)：Free algebras in the Tits-Kantor-Koecher category（Tits-Kantor-Koecher范畴中的自由代数）
报告人 (Speaker)： IRYNA KASHUBA 副教授（南方科技大学）
报告时间 (Time)：2023年11月30日(周四) 8:50-11:50
报告地点 (Place)：宝山校区F309
邀请人(Inviter)：张红莲
报告摘要：We study free algebras in the category of sl(2)-modules that are sums of copies of trivial and adjoint representations. This category is a home for Lie algebras which appear applying the celebrated Tits-Kantor-Koecher construction to Jordan algebras and therefore we call it the Tits-Kantor-Koecher category. The study of homological properties of free algebras (free associative, free commutative associative and free Lie algebra) is motivated by the conjecture of I.Kashuba and O.Mathieu that certain homologies of the free Lie algebra in TKK category vanish, which, if true, gives formulas for dimensions of homogeneous components of the free Jordan algebra. This is joint work with Vladimir Dotsenko.