Combinatorial Aspects of the Quantized Universal Enveloping Algebra of $$\mathfrak {sl}_{n+1}$$ sl n + 1

2018 ◽  
Vol 22 (4) ◽  
pp. 681-710
Author(s):  
Raymond Cheng ◽  
David M. Jackson ◽  
Geoff J. Stanley
Keyword(s):  
Universal Enveloping Algebra ◽  
Enveloping Algebra ◽  
Quantized Universal Enveloping Algebra

scholarly journals Assembling Crystals of Type A

Algebra ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Vladimir I. Danilov ◽  
Alexander V. Karzanov ◽  
Gleb A. Koshevoy
Keyword(s):  
Directed Graphs ◽  
Type A ◽  
Universal Enveloping Algebra ◽  
Combinatorial Structure ◽  
Efficient Procedure ◽  
Enveloping Algebra ◽  
Quantized Universal Enveloping Algebra

Regular An-crystals are certain edge-colored directed graphs, which are related to representations of the quantized universal enveloping algebra Uq(𝔰𝔩n+1). For such a crystal K with colors 1,2,…,n, we consider its maximal connected subcrystals with colors 1,…,n-1 and with colors 2,…,n and characterize the interlacing structure for all pairs of these subcrystals. This enables us to give a recursive description of the combinatorial structure of K via subcrystals and develop an efficient procedure of assembling K.

THE HEISENBERG FAMILY FOR THE PRINCIPAL GRADING OF $U_q(\hat{\cal G})$

2009 ◽  
Vol 23 (30) ◽  
pp. 5649-5656
Author(s):  
A. ZUEVSKY
Keyword(s):  
Universal Enveloping Algebra ◽  
Moody Algebra ◽  
Enveloping Algebra ◽  
Existence Conditions ◽  
Quantized Universal Enveloping Algebra

We describe existence conditions and explicitly construct elements for a Heisenberg family in the principal grading of the quantized universal enveloping algebra [Formula: see text] of an affine Kac–Moody algebra [Formula: see text] in the Drinfeld formulation.

scholarly journals DG Poisson algebra and its universal enveloping algebra

2016 ◽  
Vol 59 (5) ◽  
pp. 849-860 ◽  
Author(s):  
JiaFeng Lü ◽  
XingTing Wang ◽  
GuangBin Zhuang
Keyword(s):  
Poisson Algebra ◽  
Universal Enveloping Algebra ◽  
Enveloping Algebra

scholarly journals ELEMENTARY INVARIANTS FOR CENTRALIZERS OF NILPOTENT MATRICES

2009 ◽  
Vol 86 (1) ◽  
pp. 1-15 ◽  
Author(s):  
JONATHAN BROWN ◽  
JONATHAN BRUNDAN
Keyword(s):  
Lie Algebra ◽  
Characteristic Zero ◽  
Universal Enveloping Algebra ◽  
General Linear ◽  
Enveloping Algebra ◽  
Nilpotent Matrix ◽  
Nilpotent Matrices ◽  
Algebra Over A Field

AbstractWe construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the general linear Lie algebra over a field of characteristic zero. In particular, this gives a new proof of the freeness of the center, a result first proved by Panyushev, Premet and Yakimova.

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