勷勤数学•专家报告

题      目：$\delta$-type algebras

报  告  人： Ivan Kaygorodov 教授  (邀请人：张泽锐)

                                   University of Beira Interior

时      间： 7月13日  09：00-10:00

地     点：数科院东楼401

报告人简介:

       伊万·凯戈罗多夫（Ivan Kaygorodov）主要研究非结合代数与超代数，以及泊松代数的各类推广。他的工作聚焦于广义导子以及不同非结合代数簇中有限维代数的分类。他于2010年在索博列夫数学研究所（Sobolev Institute of Mathematics）获得数学博士学位。他曾在巴西工作多年，目前隶属于葡萄牙贝拉因特拉大学（University of Beira Interior）。伊万·凯戈罗多夫已在国际同行评审期刊上发表研究论文140余篇。近年来，他担任欧洲非结合代数网络（European Non-Associative Algebra Network）协调员，并组织欧洲非结合代数每周研讨会（European Non-Associative Algebra Weekly Seminar）：一个专注于非结合代数最新进展的国际在线研讨会。他同时担任《Communications in Mathematics》（Scopus Q1，SJR Q1）的主编，以及《Journal of Non-Associative Structures》的创刊主编。

摘      要：

       This talk presents a unified framework for $\delta$-type algebras, obtained by generalizing classical derivations to $\delta$-derivations satisfying the identity $D(x \cdot y)=\delta\bigl(D(x)\cdot y+x\cdot D(y)\bigr).$ We introduce $\delta$-Leibniz algebras, $\delta$-Novikov algebras, (transposed) $\delta$-Poisson algebras, and $\delta$-Novikov--Poisson algebras, and discuss the relationships among these structures. We examine both the similarities and the differences between classical algebras and their $\delta$-type counterparts. In particular, we present examples of finite-dimensional complex simple algebras of $\delta$-type for which no analogous simple objects exist in the classical setting. We also show that the commutator algebra of a $\delta$-Novikov--Poisson algebra naturally gives rise to a transposed $(\delta+1)$-Poisson algebra.

          欢迎老师、同学们参加、交流！