Cyclic homology via derived functors

Donadze, Guram; Inassaridze, Nick; Ladra, M.

doi:10.4310/hha.2010.v12.n2.a10

Cited by 4 publications

(2 citation statements)

References 18 publications

(25 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, where the horizontal differentials are obtained by alternating sums of face homomorphisms. Since K is a field, f ⊗n * → g ⊗n is an aspherical augmented simplicial vector space (see for example [8,Lemma 2.3] or [11,Lemma 2.1]), for each n ≥ 1. Therefore, we have an isomorphism:…”

Section: Definition 21 ([19]mentioning

confidence: 99%

A non-abelian exterior product and homology of Leibniz algebras

2017

Self Cite

View full text Add to dashboard Cite

Abstract. We introduce a non-abelian exterior product of two crossed modules of Leibniz algebra and investigate its relation to the low dimensional Leibniz homology. Later this non-abelian exterior product is applied to the construction of eight term exact sequence in Leibniz homology. Also its relationship to the universal quadratic functor is established, which is applied to the comparison of the second Lie and Leibniz homologies of a Lie algebra.

show abstract

Section: Definition 21 ([19]mentioning

confidence: 99%

A non-abelian exterior product and homology of Leibniz algebras

2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [9], Donadze et al obtain the generalized Hopf-type formulas for the cyclic homology of algebras, using the method of n-foldČech derived functors [7,11]. They get the exact sequence…”

Section: Free (Projective) Crossed Modules and Cyclic Homologymentioning

confidence: 99%

Projective crossed modules of algebras and cyclic homology

Ilgaz

2016

Turk J Math

View full text Add to dashboard Cite

show abstract

Higher colimits, derived functors and homology

Ivanov¹,

Mikhailov²,

Sosnilo³

2019

Sb. Math.

View full text Add to dashboard Cite

A theory of higher colimits over categories of free presentations is developed. It is shown that different homology functors such as Hoshcshild and cyclic homology of algebras over a field of characteristic zero, simplicial derived functors, and group homology can be obtained as higher colimits of simply defined functors. Connes' exact sequence linking Hochschild and cyclic homology was obtained using this approach as a corollary of a simple short exact sequence. As an application of the developed theory it is shown that the third reduced K-functor can be defined as the colimit of the second reduced K-functor applied to the fibre square of a free presentation of an algebra. A Hopf-type formula for odd dimensional cyclic homology of an algebra over a field of characteristic zero is also proved.arXiv:1805.07754v2 [math.KT]

show abstract

Cyclic homology via derived functors

Cited by 4 publications

References 18 publications

A non-abelian exterior product and homology of Leibniz algebras

A non-abelian exterior product and homology of Leibniz algebras

Projective crossed modules of algebras and cyclic homology

Higher colimits, derived functors and homology

Contact Info

Product

Resources

About