Výsledky vyhledávání - "Łukasz Kubat"

The structure monoid and algebra of a non-degenerate set-theoretic solution of the Yang–Baxter equation

Autor: Łukasz Kubat, Eric Jespers, Arne Van Antwerpen

Publikováno v: Transactions of the American Mathematical Society. 372:7191-7223

For a finite involutive non-degenerate solution $(X,r)$ of the Yang--Baxter equation it is known that the structure monoid $M(X,r)$ is a monoid of I-type, and the structure algebra $K[M(X,r)]$ over a field $K$ share many properties with commutative p

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0ac22b66018a0d2c86ba426040216884
https://doi.org/10.1090/tran/7837

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Corrigendum and addendum to 'The structure monoid and algebra of a non-degenerate set-theoretic solution of the Yang-Baxter equation'

Autor: Łukasz Kubat, Arne Van Antwerpen, Eric Jespers

One of the main results stated in Theorem 4.4 of our article, which appears in Trans. Amer. Math. Soc. 372 (2019), no. 10, 7191–7223, is that the structure algebra K [ M ( X , r ) ] K[M(X,r)] , over a field K K , of a finite bijective left non-dege

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7feb9d2ed06431dcd44d7f479266a3d3
https://hdl.handle.net/20.500.14017/331717d7-c765-4cd8-969b-a7f257871dda

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Set-theoretic solutions of the Pentagon Equation

Autor: Eric Jespers, Ilaria Colazzo, Łukasz Kubat

A set-theoretic solution of the Pentagon Equation on a non-empty set $S$ is a map $s\colon S^2\to S^2$ such that $s_{23}s_{13}s_{12}=s_{12}s_{23}$, where $s_{12}=s\times\mathrm{id}$, $s_{23}=\mathrm{id}\times s$ and $s_{13}=(\tau\times\mathrm{id})(\m

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::257519808362d40177490ed9f88bc712
http://arxiv.org/abs/2004.04028

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Factorizations of skew braces

Autor: Leandro Vendramin, Eric Jespers, Łukasz Kubat, A. Van Antwerpen

Publikováno v: CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET

We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang-Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5e4b97670ddf28987c0ff719f502c3e7
https://doi.org/10.1007/s00208-019-01909-1

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Gröbner-Shirshov Bases for Plactic Algebras

Autor: Łukasz Kubat, Jan Okniński

Publikováno v: Vrije Universiteit Brussel

A finite Grobner-Shirshov basis is constructed for the plactic algebra of rank 3 over a field K. It is also shown that plactic algebras of rank exceeding 3 do not have finite Grobner-Shirshov bases associated to the natural degree-lexicographic order

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6abffdd72f8eec4bf24aef25b8e7fd02
https://doi.org/10.1142/s1005386714000534

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Plactic algebra of rank 3

Autor: Łukasz Kubat, Jan Okniński

Publikováno v: Vrije Universiteit Brussel

The structure of the algebra K[M] of the plactic monoid M of rank 3 over a field K is studied. The minimal prime ideals of K[M] are described. There are only two such ideals and each of them is a principal ideal determined by a homogeneous congruence

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::37467fa4408511b67bc5ce7fdc11645a
https://cris.vub.be/en/publications/plactic-algebra-of-rank-3(9028fa74-fbbd-4ff3-ab3c-8cdbb04cc9a9).html

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Irreducible representations of the plactic algebra of rank four

Autor: Jan Okniński, Łukasz Kubat, Ferran Cedó

Publikováno v: Vrije Universiteit Brussel
National Information Processing Institute

Irreducible representations of the plactic monoid M of rank four are studied. Certain concrete families of simple modules over the plactic algebra K [ M ] over a field K are constructed. It is shown that the Jacobson radical J ( K [ M ] ) of K [ M ]

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::610eb5c7aaf2f9cfafd9069074765e32
https://cris.vub.be/en/publications/irreducible-representations-of-the-plactic-algebra-of-rank-four(14906d60-4bec-4672-9c33-e1f504c47fe1).html

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Irreducible representations of the Chinese monoid

Autor: Jan Okniński, Łukasz Kubat

Publikováno v: Vrije Universiteit Brussel

All irreducible representations of the Chinese monoid $C_n$, of any rank $n$, over a nondenumerable algebraically closed field $K$, are constructed. It turns out that they have a remarkably simple form and they can be built inductively from irreducib

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::165971ce86572272904e0056061031b5
https://cris.vub.be/en/publications/irreducible-representations-of-the-chinese-monoid(dbbe99cb-5490-4e15-904b-b78790faedfd).html

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Identities of the plactic monoid

Autor: Łukasz Kubat, Jan Okniński

Publikováno v: Vrije Universiteit Brussel

It is shown that the plactic monoid M of rank $3$ satisfies the identity $wvvwvw=wvwvvw$ where $v=xyyx xy xyyx$ and $w= xyyx yx xyyx$. This is accomplished by first showing that certain simple monoids related to $M$ satisfy this identity. T

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::38dacf25a1da4dc50542ddd31dd71999
https://researchportal.vub.be/en/publications/eed759c3-66f4-454b-a52a-7579f1ea3c23

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