Graded contractions of affine Lie algebras
نویسندگان
چکیده
منابع مشابه
Graded Contractions of Bilinear Invariant Forms of Lie Algebras
ABSTRACT. We introduce a new construction of bilinear invariant forms on Lie algebras, based on the method of graded contractions. The general method is described and the Z2-, Z3-, and Z2 ⊗ Z2-contractions are found. The results can be applied to all Lie algebras and superalgebras (finite or infinite dimensional) which admit the chosen gradings. We consider some examples: contractions of the Ki...
متن کاملThe Centroid of Extended Affine and Root Graded Lie Algebras
We develop general results on centroids of Lie algebras and apply them to determine the centroid of extended affine Lie algebras, loop-like and Kac-Moody Lie algebras, and Lie algebras graded by finite root systems.
متن کاملRealization of locally extended affine Lie algebras of type $A_1$
Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...
متن کاملASSOCIATED LIE ALGEBRAS AND GRADED CONTRACTIONS OF THE PAULI GRADED sl(3, C)
The grading Γ : L = ⊕ i∈I Li is a refinement of the grading Γ̃ : L = ⊕ j∈J L̃j if for each i ∈ I there exists j ∈ J such that Li ⊆ L̃j . Refinement is called proper if the cardinality of I is greater than the cardinality of the set J . Grading which cannot be properly refined is called fine. The property (2) defines a binary operation on the set I . If [Li,Lj ] = {0} holds, we can choose an arbitr...
متن کاملRepresentations of affine Lie algebras,
The author considers an elliptic analogue of the Knizhnik-Zamolodchikov equations – the consistent system of linear differential equations arising from the elliptic solution of the classical Yang-Baxter equation for the Lie algebra sl N. The solutions of this system are interpreted as traces of products of intertwining operators between certain representations of the affine Lie algebra sl N. A ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1996
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/29/14/025