Year: 2026
Type: preprint
Abstract: Let $A$ be an associative PI-algebra over a field of characteristic zero. The central polynomials of $A$ give rise to a sequence $\{χ_n^z(A)\}_{n\geq 1}$ of $S_n$-characters, called its central cocharacters. A natural problem is to understand which algebraic properties of $A$ are imposed by bounds on the multiplicities occurring in the decompositions of these cocharacters into irreducible characters. We prove that these multiplicities are bounded by one if and only if there exist scalars $(α,β)\neq(0,0)$ such that $α[x_1,x_2]x_1+βx_1[x_1,x_2]$ takes values in the center of $A$. This provides a central analogue of the Ananin-Kemer theorem for ordinary cocharacters. We also characterize the algebras whose central cocharacter multiplicities are uniformly bounded.
Source: arXiv (Cornell University)
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223208272