勷勤数学•杰出学者报告

题      目：Admissible varieties of algebras

报  告  人：Ivan Shestakov  教授  (邀请人：张泽锐)

                                 巴西圣保罗大学

时      间：12月6日  15：00-16：00

地     点：数科院西楼111报告厅

报告人简介:

         Ivan Shestakov是巴西圣保罗大学数学与统计研究所名誉教授。他是巴西科学院院士、发展中国家科学进步世界科学院院士、美国数学学会会员。2007 年，他荣获美国数学学会 E.H.Moore 研究论文奖，2017 年，他荣获索博列夫数学研究所“数学杰出贡献”金质奖章。

摘      要：

       We consider the subvarieties of  the variety of noncommutative Jordan algebras that admit  structure theories similar to those of alternative and Jordan algebras. In the case of finite dimensional algebras examples of such varieties were considered in 1960-70-s by R.Schafer, R.Block, A, Thedy and the author. Now we are trying to extend certain results on nilpotency and solvability  of infinite dimensional algebras.  A homogeneous  variety V of noncommutative Jordan algebras we call "n-admissible" if any anticommutative algebra from V is  nilpotent of index n. If any anticommutative algebra from V is locally nilpotent, we call V "locally admissible". For instance, the variety of Jordan algebras is 2-admissible,  the variety of associative algebras is 3-admissible,  the variety of alternative algebras is 4-admissible. We prove, in particular, that in a locally admissible variety  - Any nil algebra A of bounded degree is locally nilpotent,
- If the algebra A in the previous statement belongs to  an admissible variety over a field of characteristic 0, then A i is solvable,
- The nil radical of a finitely generated PI-algebra A from an admissible variety  is nilpotent,
- Any finitely generated coalgebra in an admissible variety is finite dimensional.

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