20 research outputs found
Isotropy in Group Cohomology
The analogue of Lagrangians for symplectic forms over finite groups is
studied, motivated by the fact that symplectic G-forms with a normal Lagrangian
N<G are in one-to-one correspondence, up to inflation, with bijective 1-cocycle
data on the quotients G/N. This yields a method to construct groups of central
type from such quotients, known as Involutive Yang-Baxter groups. Another
motivation for the search of normal Lagrangians comes from a non-commutative
generalization of Heisenberg liftings which require normality.
Although it is true that symplectic forms over finite nilpotent groups always
admit Lagrangians, we exhibit an example where none of these subgroups is
normal. However, we prove that symplectic forms over nilpotent groups always
admit normal Lagrangians if all their p-Sylow subgroups are of order less than
p^8
Quotient gradings and the intrinsic fundamental group
Quotient grading classes are essential participants in the computation of the
intrinsic fundamental group of an algebra . In order to study
quotient gradings of a finite-dimensional semisimple complex algebra it is
sufficient to understand the quotient gradings of twisted gradings. We
establish the graded structure of such quotients using Mackey's obstruction
class. Then, for matrix algebras we tie up the concepts of
braces, group-theoretic Lagrangians and elementary crossed products. We also
manage to compute the intrinsic fundamental group of the diagonal algebras
and .Comment: 33 page
Inductive method for separable deformations
The Donald-Flanigan conjecture asserts that any group algebra of a finite
group has a separable deformation. We apply an inductive method to deform group
algebras from deformations of normal subgroup algebras, establishing an
infinite family of metacyclic groups which fulfill the conjecture.Comment: 6 page