Local derivations of finitary incidence algebras

Khrypchenko, Mykola

doi:10.1007/s10474-017-0758-7

Cited by 13 publications

(6 citation statements)

References 27 publications

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“…A decomposition theorem for such involutions was obtained in [4]. Khrypchenko of the current article proved in [21] that each R-linear local derivation of the finitary incidence algebra F I(P, R) of a poset P over a commutative unital ring R is a derivation, generalizing (partially) a result by Nowicki and Nowosad [26].…”

Section: Introductionmentioning

confidence: 57%

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Higher Derivations of Finitary Incidence Algebras

Kaygorodov

Khrypchenko

Wei

2018

Algebr Represent Theor

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Let P be a partially ordered set, R a commutative unital ring and F I(P, R) the finitary incidence algebra of P over R. We prove that each Rlinear higher derivation of F I(P, R) decomposes into the product of an inner higher derivation of F I(P, R) and the higher derivation of F I(P, R) induced by a higher transitive map on the set of segments of P .2010 Mathematics Subject Classification. Primary 16S50, 16W25; Secondary 16G20, 06A11.

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Section: Introductionmentioning

confidence: 57%

“…The study of algebraic mappings on incidence algebras was initiated by Stanley [37]. Since then, automorphisms, involutions, derivations (and their generalizations) on incidence algebras have been actively investigated, see [1,33,7,5,6,22,34,17,18,10,40,20,41,21,2,8] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Higher Derivations of Finitary Incidence Algebras

Kaygorodov

Khrypchenko

Wei

2018

Algebr Represent Theor

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“…After, numerous new results related to the description of local and 2-local derivations of associative algebras have appeared. For example, papers [1,3,4,15,16,22] are devoted to local and 2-local derivations of associative algebras.…”

Section: Introductionmentioning

confidence: 99%

A Characterization of Derivations and Automorphisms on Some Simple Algebras

Arzikulov

Urinboyev²,

Ergasheva

2022

UMJ

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In the present paper, we study simple algebras, which do not belong to the well-known classes of algebras (associative algebras, alternative algebras, Lie algebras, Jordan algebras, etc.). The simple finite-dimensional algebras over a field of characteristic 0 without finite basis of identities, constructed by Kislitsin, are such algebras. In the present paper, we consider two such algebras: the simple seven-dimensional anticommutative algebra $\mathcal{D}$ and the seven-dimensional central simple commutative algebra $\mathcal{C}$. We prove that every local derivation of these algebras $\mathcal{D}$ and $\mathcal{C}$ is a derivation, and every 2-local derivation of these algebras $\mathcal{D}$ and $\mathcal{C}$ is also a derivation. We also prove that every local automorphism of these algebras $\mathcal{D}$ and $\mathcal{C}$ is an automorphism, and every 2-local automorphism of these algebras $\mathcal{D}$ and $\mathcal{C}$ is also an automorphism.

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“…In his paper [26] was proved that a 2-local derivation of the algebra B(H) of all bounded linear operators on the infinite-dimensional separable Hilbert space H is a derivation. After his works, appear numerous new results related to the description of local and 2-local derivations of associative algebras (see, for example, [1], [3], [4], [20], [21], [23]).…”

Section: Introductionmentioning

confidence: 99%