Algebras of conjugacy classes of partial elements

2013/10/22 by Alexeevski, Andrei V., Natanzon, Sergey M.
Engineering · Mathematics · #20F69 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1310.5860

openalex publication_date 2013/10/22 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

In 2001 Ivanov and Kerov associated with the infinite permutation group S_∞ certain commutative associative algebra A_∞ called the algebra of conjugacy classes of partial elements. A standard basis of A_∞ is labeled by Yang diagrams of all orders. Mironov, Morozov, Natanzon, 2012, have proved that the completion of A_∞ is isomorphic to the direct product of centers of group algebras of groups S_n. This isomorphism was explored in a construction of infinite dimensional Cardy-Frobenius algebra corresponding to asymptotic Hurwitz numbers. In this work algebras of conjugacy classes of partial elements are defined for a wider class of infinite groups. It is proven that completion of any such algebra is isomorphic to the direct product of centers of group algebras of relevant subgroups.

Related

• The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations
• Partial isomorphisms over finite fields
• Products of conjugacy classes in finite and algebraic simple groups
• Products and commutators of classes in algebraic groups
• Vertex algebras and the class algebras of wreath products