A supercharacter theory for involutive algebra groups

Involutive Yang-baxter Groups

In 1992 Drinfeld posed the question of finding the set-theoretic solutions of the Yang-Baxter equation. Recently, Gateva-Ivanova and Van den Bergh and Etingof, Schedler and Soloviev have shown a group-theoretical interpretation of involutive non-degenerate solutions. Namely, there is a oneto-one correspondence between involutive non-degenerate solutions on finite sets and groups of I-type. A gr...

Construction of supercharacter theories of finite groups

Much can be learned about a finite group from its character table, but sometimes that table can be difficult to compute. Supercharacter theories are generalizations of character theory, defined by P. Diaconis and I.M. Isaacs in [8], in which certain (possibly reducible) characters called supercharacters take the place of the irreducible characters, and a certain coarser partition of the group t...

Involutive Bases in the Weyl Algebra

Involutive bases are a special kind of non-reduced Gröbner bases. They have been introduced by Gerdt and collaborators for polynomial ideals (see e.g. Zharkov and Blinkov, 1993; Gerdt and Blinkov, 1998a,b) based on ideas from the Janet–Riquier theory of differential equations (Janet, 1929; Riquier, 1910). Involutive bases possess special combinatorial properties: in particular, they define Stan...

A Lie Algebra for Frölicher Groups

Frölicher spaces form a cartesian closed category which contains the category of smooth manifolds as a full subcategory. Therefore, mapping groups such as C∞(M, G) or Diff(M), but also projective limits of Lie groups are in a natural way objects of that category, and group operations are morphisms in the category. We call groups with this property Frölicher groups. One can define tangent spaces...

Topological Methods in Abstract Algebra. Cohomology Theory of Groups