Extensions Realizing Affine Datum
报告人：Alexander Wires 副教授
报告人单位：西南财经大学
报告时间：2022年06月08日（周三）下午17:00-18:00
报告地点：数学学院 西303 (线上：腾讯会议ID：906-7425-7529，无密码)
摘要：For a fixed signature, we consider the decomposition and reconstruction of extensions with kernels which support a compatible affine operation. Once the notion of affine datum is given, the extensions realizing fixed affine datum are parametrized by isomorphism classes of 2-cocycles. The resulting abelian cohomology group of extensions is a far-reaching generalization to arbitrary varieties of universal algebras of the classical development in group theory ; in addition, the cohomology group accepts an additional parameter which controls the equational theories of possible extensions of the datum. This introduces embeddings of cohomology groups determined by the lattice of subvarieties. There is a natural notion of derivation and the resulting abelian group of derivations is isomorphic to the group of stabilizing automorphism of the semidirect product.
In varieties with a difference term, the stronger equational theory allows for a characterization of central extensions by an appropriate notion of trivial compatible action. In such varieties, we establish a low-dimensional Hochschild-Serre exact sequence. We discuss covers and the possible generalizations of Schur Multipliers and the characterization by affine commutator relation algebras. Are there spectral sequences in any variety with a difference term with nontrivial abelian congruences ?
报告人简介：Alexander Wires于2013年从美国范德堡大学（全美前17名）获得数学博士学位，师从于泛代数领军人物 Ralph McKenzie教授。2013年-2015年在加拿大滑铁卢大学从事博士后研究。2015年7月以高端外国专家引进西南财经大学从事教学科研工作至今。Alexander Wires主要从事换位子理论研究，提出了换位子理论的重要猜想。在国际学术期刊《Algebra Universalis》《Discrete Mathematics》《Annals of Combinatorics》《Int.J. Algebra Comput.》等上发表了多篇高质量论文。2016年在国际学术期刊《Annals of Combinatorics》上发表的论文《Defifinability in the substructure ordering of simple graphs》被引用17次。主持过国家自然科学基金外国青年基金1项，正在主持国家自然科学基金面上项目1项。Alexander Wires荣获2021年天府友谊奖。
