scholarly journals On Injective Modules and Support Varieties for the Small Quantum Group

2010 ◽  
Author(s):  
C. M. Drupieski
Keyword(s):  
Quantum Group ◽  
Injective Modules ◽  
Small Quantum ◽  
Support Varieties

scholarly journals Modules over the small quantum group and semi-infinite flag manifold

2005 ◽  
Vol 10 (3-4) ◽  
pp. 279-362 ◽  
Author(s):  
S. Arkhipov ◽  
R. Bezrukavnikov ◽  
A. Braverman ◽  
D. Gaitsgory ◽  
I. Mirkovic
Keyword(s):  
Quantum Group ◽  
Flag Manifold ◽  
Small Quantum

scholarly journals Support Varieties and Representation Type of Small Quantum Groups

2009 ◽  
Vol 2010 (7) ◽  
pp. 1346-1362 ◽  
Author(s):  
Jörg Feldvoss ◽  
Sarah Witherspoon
Keyword(s):  
Quantum Groups ◽  
Representation Type ◽  
Small Quantum ◽  
Support Varieties

On unrolled Hopf algebras

2018 ◽  
Vol 27 (10) ◽  
pp. 1850053
Author(s):  
Nicolás Andruskiewitsch ◽  
Christoph Schweigert
Keyword(s):  
Quantum Group ◽  
Lie Algebra ◽  
Hopf Algebras ◽  
Drinfeld Module ◽  
Nichols Algebra ◽  
Small Quantum ◽  
Definition Of ◽  
Special Case

We show that the definition of unrolled Hopf algebras can be naturally extended to the Nichols algebra [Formula: see text] of a Yetter–Drinfeld module [Formula: see text] on which a Lie algebra [Formula: see text] acts by biderivations. As a special case, we find unrolled versions of the small quantum group.

scholarly journals DIAGRAMMATIC CONSTRUCTION OF REPRESENTATIONS OF SMALL QUANTUM $$ \mathfrak{sl} $$2

2021 ◽  
Author(s):  
C. BLANCHET ◽  
M. DE RENZI ◽  
J. MURAKAMI
Keyword(s):  
Quantum Group ◽  
Monoidal Category ◽  
Fundamental Representation ◽  
Combinatorial Description ◽  
Root Of Unity ◽  
Small Quantum ◽  
Odd Order

AbstractWe provide a combinatorial description of the monoidal category generated by the fundamental representation of the small quantum group of $$ \mathfrak{sl} $$ sl 2 at a root of unity q of odd order. Our approach is diagrammatic, and it relies on an extension of the Temperley–Lieb category specialized at δ = −q − q−1.

scholarly journals On semi-infinite cohomology of finite-dimensional graded algebras

2010 ◽  
Vol 146 (2) ◽  
pp. 480-496 ◽  
Author(s):  
Roman Bezrukavnikov ◽  
Leonid Positselski
Keyword(s):  
Quantum Group ◽  
General Setting ◽  
Derived Categories ◽  
Graded Algebras ◽  
Root Of Unity ◽  
Finite Dimensional ◽  
Small Quantum ◽  
Definition Of

AbstractWe describe a general setting for the definition of semi-infinite cohomology of finite-dimensional graded algebras, and provide an interpretation of such cohomology in terms of derived categories. We apply this interpretation to compute semi-infinite cohomology of some modules over the small quantum group at a root of unity, generalizing an earlier result of Arkhipov (posed as a conjecture by B. Feigin).

scholarly journals The small quantum group and the Springer resolution

2007 ◽  
pp. 89-101 ◽  
Author(s):  
R. Bezrukavnikov ◽  
A. Lachowska
Keyword(s):  
Quantum Group ◽  
Small Quantum

scholarly journals The small quantum group as a quantum double

2009 ◽  
Vol 322 (7) ◽  
pp. 2580-2585 ◽  
Author(s):  
Pavel Etingof ◽  
Shlomo Gelaki
Keyword(s):  
Quantum Group ◽  
Quantum Double ◽  
Small Quantum

scholarly journals On the center of the small quantum group

2003 ◽  
Vol 262 (2) ◽  
pp. 313-331 ◽  
Author(s):  
Anna Lachowska
Keyword(s):  
Quantum Group ◽  
Small Quantum
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