中俄数学中心讨论班——Stack Algebras: Simplicity and Nilpotency

• 主讲人：Artem Lopatin (UNICAMP)
• 时间： 2026-10-14 15:00 - 2026-10-14 15:50
• 地点： Room 209, ZhiHua Building

 

Abstract：

We introduce and study the variety of stack algebras, defined by the identity [x(yz) = \lambda (xy)z + \mu (xz)y. ]

Several families of examples are constructed, including matrix-type examples, and all two-dimensional stack algebras are classified. A key structural result shows that every nonassociative word in a stack algebra can be expressed as a linear combination of left-normed words. This leads to general results on nilpotency, including bounds for the nilpotency degree, a description of null-filiform stack algebras, and parameter conditions implying the identity A^4=0.

We also classify finite-dimensional simple stack algebras over an arbitrary field: every such algebra is classically simple, namely, either a simple associative algebra or a simple Lie algebra. In particular, there are no finite-dimensional nonclassically simple stack algebras. Finally, we compare the variety of stack algebras with several classical varieties of nonassociative algebras, including alternative, noncommutative Jordan, and Novikov algebras.