Relative Cellular Algebras

Ehrig, Michael; Tubbenhauer, Daniel

doi:10.1007/s00031-019-09544-5

Cited by 8 publications

(6 citation statements)

References 30 publications

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“…Proof The proof is not very different from the general theory as in [1, 6, 8, 10, 17, 21, 22]. In particular, the result is just a (graded) reformulation of [10, Theorem 3; 22, Section 2C].…”

Section: Sandwich Cellular Algebrasmentioning

confidence: 85%

Cellularity for weighted KLRW algebras of types B$B$, A(2)$A^{(2)}$, D(2)$D^{(2)}$

Mathas

Tubbenhauer

2022

Journal of London Math Soc

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This paper constructs homogeneous affine sandwich cellular bases of weighted KLRW algebras in types BZ⩾0$B_{\mathbb {Z}_{\geqslant 0}}$, A2·e(2)$A^{(2)}_{2\cdot e}$, De+1(2)$D^{(2)}_{e+1}$. Our construction immediately gives homogeneous sandwich cellular bases for the finite‐dimensional quotients of these algebras. Since weighted KLRW algebras generalize KLR algebras, we also obtain bases and cellularity results for the (infinite and finite‐dimensional) KLR algebras.

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Section: Sandwich Cellular Algebrasmentioning

confidence: 85%

Cellularity for weighted KLRW algebras of types B$B$, A(2)$A^{(2)}$, D(2)$D^{(2)}$

Mathas

Tubbenhauer

2022

Journal of London Math Soc

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“…We also study a generalization of cellularity in Section 2, giving us a toolkit to parameterize the simples modules of the aforementioned algebras. Note hereby that this generalization heavily builds on and borrows from [Gr51], [KX99], [GW15] or [ET21]. Although it might be known to experts, our exposition is new.…”

Section: (B)mentioning

confidence: 99%

“…Remark 2.3 One of the advantages of the basis-focused formulation above is that Definition 2.2 works, mutatis mutandis, for relative cellular algebras as in [ET21] or (strictly object-adapted) cellular categories [Wes09], [EL16].…”

Section: A Generalization Of Cellularitymentioning

confidence: 99%

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Handlebody diagram algebras

Tubbenhauer,

Vaz

2021

Preprint

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In this paper we study handlebody versions of classical diagram algebras, most prominently, handlebody versions of Temperley-Lieb, blob, Brauer/BMW, Hecke and Ariki-Koike algebras. Moreover, motivated by Green-Kazhdan-Lusztig's theory of cells, we reformulate the notion of (sandwich, inflated or affine) cellular algebras. We explain this reformulation and how all of the above algebras are part of this theory. Contents1. Introduction 1 2. A generalization of cellularity 4 3. Handlebody braid and Coxeter groups 11 4. Handlebody Temperley-Lieb and blob algebras 16 5. Handlebody Brauer and BMW algebras 28 6. Handlebody Hecke and Ariki-Koike algebras 36 References 41

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“…There are several generalizations of cellular algebras. For example, affine cellular algebras if we extend the framework of cellular algebras to algebras that need not be finite dimensional over a field [13], relative cellular algebras if we allow different partial orderings relative to fixed idempotents [4], standardly based algebra by constructing a nice bases satisfy some conditions [3] and almost cellular algebras if we remove the compatible anti-involution from the definition of cellularity [7]. In this paper, we focus on the third generalization.…”

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confidence: 99%