Yang-baxter operators arising from (co)algebra structures

Dăscălescu, S.; Nichita, Florin F.

doi:10.1080/00927879908826793

Cited by 29 publications

(45 citation statements)

References 2 publications

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“…In particular it is used there to insure an algebra structure on multiple products of a monad, generalising the cases considered in Nuss [22] (see 3.8) and Menini and Stefan [19]. Yang-Baxter operators in context with algebras, coalgebras and entwinings are also studied by Brzeziński, Dǎscǎlescu and Nichita in [21], [13], [8].…”

Section: 9mentioning

confidence: 99%

Lifting Theorems for Tensor Functors on Module Categories

Wisbauer

2011

J. Algebra Appl.

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Any (co)ring R is an endofunctor with (co)multiplication on the category of abelian groups. These notions were generalised to monads and comonads on arbitrary categories. Starting around 1970 with papers by Beck, Barr and others a rich theory of the interplay between such endofunctors was elaborated based on distributive laws between them and Applegate's lifting theorem of functors between categories to related (co)module categories. Curiously enough some of these results were not noticed by researchers in module theory and thus notions like entwining structures and smash products between algebras and coalgebras were introduced (in the nineties) without being aware that these are special cases of the more general theory.The purpose of this survey is to explain several of these notions and recent results from general category theory in the language of elementary module theory focussing on functors between module categories given by tensoring with a bimodule. This provides a simple and systematic approach to smash products, wreath products, corings and rings over corings (C-rings). We also highlight the relevance of the Yang-Baxter equation for the structures on the threefold tensor product of algebras or coalgebras (see 3.6).

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Section: 9mentioning

confidence: 99%

Lifting Theorems for Tensor Functors on Module Categories

Wisbauer

2011

J. Algebra Appl.

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“…In this section, we recall results from [1] and we follow the terminology used there. For a k-vector space V , the flip map T : …”

Section: Yang-baxter Operators Arising From Algebra Structuresmentioning

confidence: 99%

“…The following theorem determines the situations where this map is a Yang-Baxter operator. Theorem 2.3 (Dȃscȃlescu-Nichita [1]). Let A be a k-algebra of dimension at least 2 and let x, y, z ∈ k be scalars.…”

Section: Yang-baxter Operators Arising From Algebra Structuresmentioning

confidence: 99%

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Yang–Baxter Operators Arising from Algebra Structures and the Alexander Polynomial of Knots

Massuyeau

Nichita

2005

Communications in Algebra

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“…It is imperative to note that the Yang-Baxter operators presented here are obtained from algebra structures, and are therefore distinct from the R-matrices that arise from quasitriangular Hopf algebras. See [2,9,10,11] for ordinary Yang-Baxter operators, [10] for one-parameter form of the QYBE, [8,10] for the coloured QYBE, [4,16] for Yang-Baxter maps and [13,15] for coloured quantum groups.…”

Section: Introductionmentioning

confidence: 99%

Spectral-Parameter Dependent Yang–Baxter Operators and Yang–Baxter Systems From Algebra Structures

Nichita

Parashar

2006

Communications in Algebra

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Abstract. For any algebra two families of coloured Yang-Baxter operators are constructed, thus producing solutions to the two-parameter quantum Yang-Baxter equation. An open problem about a system of functional equations is stated. The matrix forms of these operators for two and three dimensional algebras are computed. A FRT bialgebra for one of these families is presented. Solutions for the one-parameter quantum Yang-Baxter equation are derived and a Yang-Baxter system constructed.

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Yang-baxter operators arising from (co)algebra structures

Cited by 29 publications

References 2 publications

Lifting Theorems for Tensor Functors on Module Categories

Lifting Theorems for Tensor Functors on Module Categories

Yang–Baxter Operators Arising from Algebra Structures and the Alexander Polynomial of Knots

Spectral-Parameter Dependent Yang–Baxter Operators and Yang–Baxter Systems From Algebra Structures

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