Inverse semigroup cohomology and crossed module extensions of semilattices of groups by inverse semigroups

2021/04/27 by Mikhailo Dokuchaev, Mykola Khrypchenko, Dokuchaev, Mikhailo +3
Mathematics · #20M30 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Primary: 20M18 #secondary: 20M50

paper · pdf · doi:10.48550/arxiv.2104.13481

openalex publication_date 2021/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define and study the notion of a crossed module over an inverse semigroup and the corresponding 4-term exact sequences, called crossed module extensions. For a crossed module A over an F-inverse monoid T, we show that equivalence classes of admissible crossed module extensions of A by T are in a one-to-one correspondence with the elements of the cohomology group H³_≤(T¹,A¹).

Related

• Crossed modules and symmetric cohomology of groups
• The third cohomology group classifies crossed module extensions
• Group cohomology with coefficients in a crossed-module
• Homology and cohomology of crossed products by inverse monoid actions and Steinberg algebras
• Group Extensions of the Co-type of a Crossed Module and Strict Categorical Groups