The Department of Mathematics at Western Michigan University will present an algebra seminar on Mondays.

**Day and time: Mondays, 4 p.m.**

**Place: 6625 Everett Tower**

The purpose of the Algebra Seminar this semester is to present an outline of the theory of complex semi-simple Lie algebras. The main goal is to reach the point where a novice can understand some structure theory of classical Lie groups and Lie algebras using Dynkin diagrams. A secondary goal is to understand the representation theory of complex semisimple Lie algebras. (These two goals are closely related.) Since this theory motivates or underlies many areas of contemporary research, students who plan to pursue a career in algebra or geometry are strongly urged to attend the Seminar.

The prerequisites for the Seminar are undergraduate abstract algebra and undergraduate linear algebra.

Other resources will be posted and/or shared separately, so please be sure to let Dr. Clifton E. Ealy Jr. know if you are interested in the seminar but were not able to attend the organizational meeting in September.

**Fall 2017**

**Sept. 11**

**Organizational Meeting **presented by Clifton E. Ealy, Jr., Ph.D., Department of Mathematics, Western Michigan University

Abstract: This academic year the main thrust of the seminar will be Fusion Systems! But talks on other topics related to coding theory or algebraic geometry are welcomed. Historically, Fusion Systems arose in looking for conditions which tell us when a finite group, G, is not simple. For example, Burnside’s Theorem: If P ε Sylp(G) and P is a subgroup of Z(N G(P)), then G has a normal subgroup, H, such that G= H⋊P. Another example is Frobenius’s Normal p-complement Theorem: Let P ε Sylp(G). Then G= H⋊P if and only if N G(S) has a normal p-complement for every non-identity p-subgroup S of G. On the other hand, Frobenius’s Theorem on Frobenius groups: If G is transitive permutation group such that Gxy=1 whenever x≠y and H is the set of fixed point free elements of G with 1 included, then H is a subgroup of G and G= H⋊Gx., played an important role in the development of Fusion Systems. So, the Seminar maybe viewed as a continuation of last years Algebra Seminar . The seminar in the main will be based on David Cravens text: The Theory of Fusion Systems. But other references are Aschbacher and Oliver paper “Fusion Systems”, Bulletin of the AMS 10/2016; Aschbacher, Kessar, and Oliver’s text: Fusion Systems in Algebra and Topology; and the text: Finite Groups III, Chapter 10, Local Finite Group Theory by Huppert & Blackburn.

All are welcomed

**Sept. 18**

**Sharply 2-transitive groups I **presented by Clifton E. Ealy, Jr., Ph.D., Department of Mathematics, Western Michigan University

Abstract: In this talk we will review sharply 2-transitive groups, near-fields and near-domains, as introduced in the Algebra Seminar during the academic year 2016-2017.

All are welcomed