scholarly journals Classification of irreducible modules for Bershadsky–Polyakov algebra at certain levels

2020 ◽  
pp. 2150102
Author(s):  
Dražen Adamović ◽  
Ana Kontrec
Keyword(s):  
Representation Theory ◽  
Two Dimensional ◽  
Indecomposable Modules ◽  
Irreducible Modules ◽  
Zhu Algebra

We study the representation theory of the Bershadsky–Polyakov algebra [Formula: see text]. In particular, Zhu algebra of [Formula: see text] is isomorphic to a certain quotient of the Smith algebra, after changing the Virasoro vector. We classify all modules in the category [Formula: see text] for the Bershadsky–Polyakov algebra [Formula: see text] for [Formula: see text]. In the case [Formula: see text], we show that the Zhu algebra [Formula: see text] has two-dimensional indecomposable modules.

scholarly journals The representation theory of seam algebras

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
Alexis Langlois-Rémillard ◽  
Yvan Saint-Aubin
Keyword(s):  
Representation Theory ◽  
Boundary Conditions ◽  
Large Class ◽  
Large Family ◽  
Two Dimensional ◽  
Irreducible Modules ◽  
Composition Factors ◽  
Exact Sequences

The boundary seam algebras \mathsf{b}_{n,k}(\beta=q+q^{-1})𝖻n,k(β=q+q−1) were introduced by Morin-Duchesne, Ridout and Rasmussen to formulate algebraically a large class of boundary conditions for two-dimensional statistical loop models. The representation theory of these algebras \mathsf{b}_{n,k}(\beta=q+q^{-1})𝖻n,k(β=q+q−1) is given: their irreducible, standard (cellular) and principal modules are constructed and their structure explicited in terms of their composition factors and of non-split short exact sequences. The dimensions of the irreducible modules and of the radicals of standard ones are also given. The methods proposed here might be applicable to a large family of algebras, for example to those introduced recently by Flores and Peltola, and Crampé and Poulain d’Andecy.

On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space

2020 ◽  
Vol 14 (6) ◽  
pp. 1232-1239
Author(s):  
P. M. Pustovoit ◽  
E. G. Yashina ◽  
K. A. Pshenichnyi ◽  
S. V. Grigoriev
Keyword(s):  
Dimensional Space ◽  
Two Dimensional

scholarly journals Primitive ideals, twisting functors and star actions for classical Lie superalgebras

2016 ◽  
Vol 2016 (718) ◽  
Author(s):  
Kevin Coulembier ◽  
Volodymyr Mazorchuk
Keyword(s):  
Representation Theory ◽  
Lie Superalgebras ◽  
Simple Modules ◽  
Primitive Ideals

AbstractWe study three related topics in representation theory of classical Lie superalgebras. The first one is classification of primitive ideals, i.e. annihilator ideals of simple modules, and inclusions between them. The second topic concerns Arkhipov’s twisting functors on the BGG category

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