We define the product of admissible abstract kernels of the form φ: M → End(G)/Inn(G), where M is a monoid, G is a group and φ is a monoid homomorphism. Identifying C-equivalent abstract kernels, where C is the center of G, we obtain that the set M(M,C) of C-equivalence classes of admissible abstract kernels inducing the same action of M on C is a commutative monoid. Considering the submonoid L(M,C) of abstract kernels that are induced by special Schreier extensions, we prove that the factor monoid (M,C) = M(M,C) L(M,C) is an abelian group. Moreover, we show that this abelian group is isomorphic to the third cohomology group H3(M,C).

The third cohomology group of a monoid and admissible abstract kernels / N. Martins-Ferreira, A. Montoli, A. Patchkoria, M. Sobral. - In: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION. - ISSN 0218-1967. - 32:5(2022), pp. 1009-1041. [10.1142/S0218196722500436]

The third cohomology group of a monoid and admissible abstract kernels

A. Montoli
Secondo
;
2022

Abstract

We define the product of admissible abstract kernels of the form φ: M → End(G)/Inn(G), where M is a monoid, G is a group and φ is a monoid homomorphism. Identifying C-equivalent abstract kernels, where C is the center of G, we obtain that the set M(M,C) of C-equivalence classes of admissible abstract kernels inducing the same action of M on C is a commutative monoid. Considering the submonoid L(M,C) of abstract kernels that are induced by special Schreier extensions, we prove that the factor monoid (M,C) = M(M,C) L(M,C) is an abelian group. Moreover, we show that this abelian group is isomorphic to the third cohomology group H3(M,C).
abstract kernel; Eilenberg-Mac Lane cohomology of monoids; Monoid; Schreier extension
Settore MAT/02 - Algebra
https://www.worldscientific.com/doi/10.1142/S0218196722500436
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/945640
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