Tilting Modules for the Symplectic Blob Algebra

2011/11/01 by Andrew Reeves, Reeves, Andrew · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1111.0146

openalex publication_date 2011/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \Field be an algebraically closed field. For n ∈ ℕ and δ, δ_L, δ_R, κ_L, κ_R, κ∈ \Field, the symplectic blob algebra \sba(δ, δ_L, δ_R, κ_L, κ_R, κ) is a finite dimensional non-commutative \Field-algebra that may be viewed as an extension of the Temperley-Lieb algebra. In a previous paper, we defined, for any n ∈ ℕ, a tensor space module \tensor[_\sba]V(n). In this paper we generalise an argument used by Martin and Ryom-Hansen in their study of the (ordinary) blob algebra to show that when \sba is quasihereditary the module \tensor[_\sba]V(n) is full-tilting.

Cited by

• Calibrated representations of two boundary Temperley-Lieb algebras

Related

• A Tensor Space Representation of the Symplectic Blob Algebra
• Virtual algebraic Lie theory: Tilting modules and Ringel duals for blob algebras
• Indecomposable tilting modules for the blob algebra
• Relative contravariantly finite subcategories and relative tilting modules
• A construction of Gorenstein projective tau-tilting modules