Signed brauer's algebras

Parvathi, M.; Kamaraj, M.

doi:10.1080/00927879808826168

Cited by 22 publications

(8 citation statements)

References 9 publications

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“…Finally, we remark that other variants of signed and cyclotomic Brauer algebras, G-Brauer algebras and cyclotomic BMW have been studied previously in the papers [CGW05], [GH], [HO01], [PK98], [PK02], [PS02], [RY04]. In [Naz96], Nazarov introduced an affine analogue of the Brauer algebra which he called the (degenerate) affine Wenzl algebra.…”

Section: §1 Introductionmentioning

confidence: 98%

Cyclotomic Nazarov-Wenzl Algebras

Ariki¹,

Mathas²,

Rui³

2006

Nagoya Mathematical Journal

256

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Abstract. Nazarov [Naz96] introduced an infinite dimensional algebra, which he called the affine Wenzl algebra, in his study of the Brauer algebras. In this paper we study certain "cyclotomic quotients" of these algebras. We construct the irreducible representations of these algebras in the generic case and use this to show that these algebras are free of rank r n (2n − 1)!! (when Ω is u-admissible). We next show that these algebras are cellular and give a labelling for the simple modules of the cyclotomic Nazarov-Wenzl algebras over an arbitrary field. In particular, this gives a construction of all of the finite dimensional irreducible modules of the affine Wenzl algebra.

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Section: §1 Introductionmentioning

confidence: 98%

Cyclotomic Nazarov-Wenzl Algebras

Ariki¹,

Mathas²,

Rui³

2006

Nagoya Mathematical Journal

256

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“…Walled Brauer algebra is a subalgebra of Brauer algebra introduced by [2]. This motivated Kethesan [9], to introduce walled signed Brauer algebras which are subalgebras of signed Brauer algebras introduced by [14]. Walled signed Brauer algebra is an algebra consisting of walled signed Brauer diagrams as basis.…”

Section: Introductionmentioning

confidence: 99%

Cellularity and representations of walled cyclic $G$-Brauer algebras

Tamilselvi¹

2020

Malaya J. Mat

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“…Multiplication is induced by concatenation of diagrams, where each arising free loop component gives rise to an additional multiplication with the indeterminate x. A signed variant of Brauer algebras has been studied in [22]. Brauer algebras play an important role in knot theory, where, for instance, Birman-Murakami-Wenzl algebras [5,21,26], which are the quantized version of Brauer algebras, have been used to construct generalizations of the Jones polynomial.…”

Section: Introductionmentioning

confidence: 99%

The Chromatic Brauer Category and Its Linear Representations

Müller

Wrazidlo

2020

Appl Categor Struct

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The Brauer category is a symmetric strict monoidal category that arises as a (horizontal) categorification of the Brauer algebras in the context of Banagl’s framework of positive topological field theories (TFTs). We introduce the chromatic Brauer category as an enrichment of the Brauer category in which the morphisms are component-wise labeled. Linear representations of the (chromatic) Brauer category are symmetric strict monoidal functors into the category of real vector spaces and linear maps equipped with the Schauenburg tensor product. We study representation theory of the (chromatic) Brauer category, and classify all its faithful linear representations. As an application, we use indices of fold lines to construct a refinement of Banagl’s concrete positive TFT based on fold maps into the plane.

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Signed brauer's algebras

Cited by 22 publications

References 9 publications

Cyclotomic Nazarov-Wenzl Algebras

Cyclotomic Nazarov-Wenzl Algebras

Cellularity and representations of walled cyclic $G$-Brauer algebras

The Chromatic Brauer Category and Its Linear Representations

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