0-Cohomology of Semigroups

Novikov, B. V.

doi:10.1016/s1570-7954(07)05004-8

Cited by 5 publications

(9 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The theory of partial projective representations is strongly related to Exel's semigroup S(G). In fact, they can be alternatively defined via projective representations of S(G), so that the theory of projective representations of semigroups and their Schur multipliers, elaborated by Novikov in [238][239][240] (see also [241]), comes into the picture as an essential working tool. The usual cohomology of semigroups does not serve the projective semigroup representations, instead the more general 0-cohomology [240] fits them with its natural partial flavor.…”

Section: Mathematics Subject Classificationmentioning

confidence: 99%

Recent developments around partial actions

Dokuchaev

2018

São Paulo J. Math. Sci.

View full text Add to dashboard Cite

We give an overview of publications on partial actions and related concepts, paying main attention to some recent developments on diverse aspects of the theory, such as partial actions of semigroups, of Hopf algebras and groupoids, the globalization problem for partial actions, Morita theory of partial actions, twisted partial actions, partial projective representations and the Schur multiplier, cohomology theories related to partial actions, Galois theoretic results, ring theoretic properties and ideals of partial crossed products. Among the applications we consider in more detail the case of the Carlsen-Matsumoto C *-algebra related to an arbitrary subshift, but also mention many others. The total number of publications directly related to partial actions and partial representations is more than 130, so that it is impossible even to describe briefly the content of all of them within the constraints of the present survey. Thus, the majority of them are only cited with respects to specific topics, trying to give an idea about the involved matter. In order to complete the picture, we refer the reader to a recent book by Ruy Exel, to our previous surveys, as well as to those by other authors.

show abstract

Section: Mathematics Subject Classificationmentioning

confidence: 99%

Recent developments around partial actions

Dokuchaev

2018

São Paulo J. Math. Sci.

View full text Add to dashboard Cite

show abstract

“…Corollaries 2 and 3 show how the multiplier of a semigroup is constructed from such components. An appropriate theory of cohomology (0-cohomology of semigroups) was developed in [19] (see also [20]). …”

Section: Lemma 4 the Group M I (S) Consists Of The Factor Sets ρ Formentioning

confidence: 99%

“…The maps (17)- (19) determine an action T on G × G. Thus G × G becomes a T -set and Theorem 4 can be restated as follows:…”

Section: The Semigroup Tmentioning

confidence: 99%

Partial projective representations and partial actions

Dokuchaev

Novikov

2010

Journal of Pure and Applied Algebra

Self Cite

View full text Add to dashboard Cite

show abstract

“…A monoid with zero is an ordinary monoid with a two-sided absorbing element, called the zero. Such structures obviously occur in ring theory (the multiplicative monoid of an associative ring with unit is a monoid with zero), but they are also used to solve some (co)homological problems [25,26], and mainly in the study of ideal extensions of semigroups [2,9,10].…”

Section: Monoids With Zeromentioning

confidence: 99%

Möbius inversion formula for monoids with zero

2010

View full text Add to dashboard Cite

The Möbius inversion formula, introduced during the 19th century in number theory, was generalized to a wide class of monoids called locally finite such as the free partially commutative, plactic and hypoplactic monoids for instance. In this contribution are developed and used some topological and algebraic notions for monoids with zero, similar to ordinary objects such as the (total) algebra of a monoid, the augmentation ideal or the star operation on proper series. The main concern is to extend the study of the Möbius function to some monoids with zero, i.e., with an absorbing element, in particular the so-called Rees quotients of locally finite monoids. Some relations between the Möbius functions of a monoid and its Rees quotient are also provided.

show abstract

0-Cohomology of Semigroups

Cited by 5 publications

References 36 publications

Recent developments around partial actions

Recent developments around partial actions

Partial projective representations and partial actions

Möbius inversion formula for monoids with zero

Contact Info

Product

Resources

About