pbw theorem
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Author(s):  
Yuqun Chen ◽  
Ivan Shestakov ◽  
Zerui Zhang
Keyword(s):  

2020 ◽  
Vol 25 (4) ◽  
pp. 1371-1385
Author(s):  
YAPING YANG ◽  
GUFANG ZHAO
Keyword(s):  

2019 ◽  
Vol 303 (2) ◽  
pp. 605-667
Author(s):  
Camille Laurent-Gengoux ◽  
Yannick Voglaire
Keyword(s):  

2018 ◽  
Vol 500 ◽  
pp. 153-170 ◽  
Author(s):  
L.A. Bokut ◽  
Yuqun Chen ◽  
Zerui Zhang
Keyword(s):  

2018 ◽  
Vol 2019 (18) ◽  
pp. 5811-5853 ◽  
Author(s):  
Simon M Goodwin ◽  
Lewis W Topley

Abstract Let ${\mathbb{k}}$ be an algebraically closed field of characteristic p > 0 and let G be a connected reductive algebraic group over ${\mathbb{k}}$. Under some standard hypothesis on G, we give a direct approach to the finite W-algebra $U(\mathfrak{g},e)$ associated to a nilpotent element $e \in \mathfrak{g} = \textrm{Lie}\ G$. We prove a PBW theorem and deduce a number of consequences, then move on to define and study the p-centre of $U(\mathfrak{g},e)$, which allows us to define reduced finite W-algebras $U_{\eta}(\mathfrak{g},e)$ and we verify that they coincide with those previously appearing in the work of Premet. Finally, we prove a modular version of Skryabin’s equivalence of categories, generalizing recent work of the second author.


2016 ◽  
Vol 23 (02) ◽  
pp. 303-324 ◽  
Author(s):  
Chunrui Ai ◽  
Shilin Yang

A class of two-parameter quantum algebras [Formula: see text] is constructed. It is shown that [Formula: see text] is a Hopf superalgebra. Then the PBW basis of [Formula: see text] is described. For this purpose, some commutative relations of root vectors of [Formula: see text] are given.


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