Combinatorics & algebra seminar-Graded Automorphisms of Skew-Symmetric Poisson Polynomial Algebras
Monday, November 2, 2026
4:00 pm - 5:00 pm
Title: Graded Automorphisms of Skew-Symmetric Poisson Polynomial Algebras
Speaker: Charlene Houchins, GWU
Date and time: Monday, November 2, 4–5pm
Place: Rome 459
Abstract: Given a multiplicative skew-symmetric matrix, we can consider the multi-parameter quantum affine n-space, a noncommutative algebra whose product is defined by entries of the matrix. Alev and Chamarie initially computed the automorphism groups of the quantum affine n-space under certain constraints on the parameter matrix. In 2025, Hai Jin generalized all graded automorphism groups of a quantum affine space for all n. If we take the semiclassical limit of the quantum affine n-space, we get a Poisson analogue with an associated additive skew-symmetric matrix. We consider all graded automorphisms of the Poisson algebra, using techniques from Jin's paper. We then use integer partitions to consider different cases of the parameter matrix to explore explicit sections of short exact sequences which give us a semidirect product.
Admission