scholarly journals Witten Volume Formulas for Semi-Simple Lie Algebras

Integers ◽  
2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Jianqiang Zhao
Keyword(s):  
Lie Algebras ◽  
Dedekind Sums ◽  
Combinatorial Method ◽  
Simple Lie Algebras ◽  
Higher Dimensional

AbstractIn this paper we provide an algebraic derivation of the explicit Witten volume formulas for a few semi-simple Lie algebras by combining a combinatorial method with the ideas used by Gunnells and Sczech in the computation of higher-dimensional Dedekind sums.

EXPLICIT TRIGONOMETRIC YANG-BAXTERIZATION

1991 ◽  
Vol 06 (21) ◽  
pp. 3735-3779 ◽  
Author(s):  
MO-LIN GE ◽  
YONG-SHI WU ◽  
KANG XUE
Keyword(s):  
Quantum Group ◽  
Lie Algebras ◽  
Braid Group ◽  
Classical Limit ◽  
Group Representation ◽  
Direct Method ◽  
Explicit Solutions ◽  
Simple Lie Algebras ◽  
Higher Dimensional

We present an explicit prescription for trigonometric Yang-Baxterization. Given a braid group representation (BGR) in appropriate form, our prescription generates explicit solutions to the quantum Yang-Baxter equations (QYBE). We have proved the correctness of this prescription, together with a variation of it, for BGR’s having two or three unequal eigenvalues. All the known explicit results obtained by Jimbo and Bazhanov are reproduced. More YB solutions are obtained from “standard” BGR’s associated with fundamental and higher dimensional representations of simple Lie algebras. Our prescription also applies to the new “nonstandard” BGR’s, which are beyond the reach of present quantum group techniques but obtainable by our previous direct method. New explicit examples include the standard ones with 6 of SU(3), 10 of SU(5) and exotic ones with C2 and D2, etc. The classical limit of our YB solutions is also studied. It turns out that some of our exotic QYB solutions have an unusual classical limit. Our results suggest that the QYBE embodies a much richer structure than we thought.

scholarly journals CODES, S-STRUCTURES, AND EXCEPTIONAL LIE ALGEBRAS

2019 ◽  
Vol 62 (S1) ◽  
pp. S14-S27 ◽  
Author(s):  
ISABEL CUNHA ◽  
ALBERTO ELDUQUE
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras ◽  
Nonassociative Algebras ◽  
Exceptional Lie Algebras

AbstractThe exceptional simple Lie algebras of types E7 and E8 are endowed with optimal $\mathsf{SL}_2^n$ -structures, and are thus described in terms of the corresponding coordinate algebras. These are nonassociative algebras which much resemble the so-called code algebras.

Models of isotropic simple lie algebras

1979 ◽  
Vol 7 (17) ◽  
pp. 1835-1875 ◽  
Author(s):  
B.N. Allison
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras

Nilpotent Orbits in Simple Lie Algebras and their Transverse Poisson Structures

2008 ◽  
Author(s):  
P. A. Damianou ◽  
H. Sabourin ◽  
P. Vanhaecke ◽  
Rui Loja Fernandes ◽  
Roger Picken
Keyword(s):  
Lie Algebras ◽  
Poisson Structures ◽  
Nilpotent Orbits ◽  
Simple Lie Algebras

scholarly journals On the construction of simple lie algebras

1973 ◽  
Vol 27 (1) ◽  
pp. 158-183 ◽  
Author(s):  
S Berman
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras
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