ROOT SYSTEMS ARISING FROM AUTOMORPHISMS

2012 ◽  
Vol 11 (03) ◽  
pp. 1250057 ◽  
Author(s):  
SAEID AZAM ◽  
MALIHE YOUSOSFZADEH
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Affine Lie Algebras ◽  
Combinatorial Approach ◽  
Reflection Algebras ◽  
Affine Root Systems ◽  
Outstanding Work ◽  
Affine Reflection

We study a combinatorial approach of producing new root systems from the old ones in the context of affine root systems and their new generalizations. The appearance of this approach in the literature goes back to the outstanding work of Kac in the realization of affine Kac–Moody Lie algebras. In recent years, this approach has been appeared in many other works, including the study of affinization of extended affine Lie algebras and invariant affine reflection algebras.

Combinatorics of extended affine root systems (type A1)

2019 ◽  
Vol 18 (03) ◽  
pp. 1950051
Author(s):  
Saeid Azam ◽  
Zahra Kharaghani
Keyword(s):  
Weyl Group ◽  
Lie Algebras ◽  
Root Systems ◽  
Extended Version ◽  
Type Formula ◽  
Exchange Condition ◽  
Affine Root Systems ◽  
Affine Reflection ◽  
Natural Way

We establish extensions of some important features of affine theory to affine reflection systems (extended affine root systems) of type [Formula: see text]. We present a positivity theory which decomposes in a natural way the nonisotropic roots into positive and negative roots, then using that, we give an extended version of the well-known exchange condition for the corresponding Weyl group, and finally give an extended version of the Bruhat ordering and the [Formula: see text]-Lemma. Furthermore, a new presentation of the Weyl group in terms of the parity permutations is given, this in turn leads to a parity theorem which gives a characterization of the reduced words in the Weyl group. All root systems involved in this work appear as the root systems of certain well-studied Lie algebras.

Extended affine Lie algebras and their root systems

1997 ◽  
Vol 126 (603) ◽  
pp. 0-0 ◽  
Author(s):  
Bruce N. Allison ◽  
Saeid Azam ◽  
Stephen Berman ◽  
Yun Gao ◽  
Arturo Pianzola
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Affine Lie Algebras

scholarly journals Classification of Quantum Tori with Involution

2002 ◽  
Vol 45 (4) ◽  
pp. 711-731 ◽  
Author(s):  
Yoji Yoshii
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Type A ◽  
Affine Lie Algebras ◽  
Precise Information ◽  
Quantum Tori ◽  
Type C

AbstractQuantum tori with graded involution appear as coordinate algebras of extended affine Lie algebras of type A1, C and BC. We classify them in the category of algebras with involution. From this, we obtain precise information on the root systems of extended affine Lie algebras of type C.

A class of non-standard modules for affine Lie algebras

1987 ◽  
Vol 196 (3) ◽  
pp. 303-313 ◽  
Author(s):  
Nolan R. Wallach
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras

QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA

1992 ◽  
Vol 07 (20) ◽  
pp. 4885-4898 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Lie Algebras ◽  
Free Field ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Hamiltonian Reduction ◽  
Affine Lie Algebras ◽  
Quantum Hamiltonian Reduction ◽  
Free Field Realization ◽  
Coset Construction ◽  
Quantum Hamiltonian

We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

scholarly journals Braided Tensor Categories of Admissible Modules for Affine Lie Algebras

2018 ◽  
Vol 362 (3) ◽  
pp. 827-854 ◽  
Author(s):  
Thomas Creutzig ◽  
Yi-Zhi Huang ◽  
Jinwei Yang
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Tensor Categories
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