Twisted cocycles of lie algebras and corresponding invariant functions

Twisted Toroidal Lie Algebras

Using n finite order automorphisms on a simple complex Lie algebra we construct twisted n-toroidal Lie algebras. Thus obtaining Lie algebras wich have a rootspace decomposition. For the case n = 2 we list certain simple Lie algebras and their automorphisms, which produce twisted 2-toroidal algebras. In this way we obtain Lie algebras that are related to all Extended Affine Root Systems of K. Sa...

Twisted Lie Algebras and Idempotent of Dynkin

In this paper we define a Dynkin idempotent for twisted Hopf algebras and generalize the results of Patras and Reutenauer in the classical case. We treat as a special case the free Lie algebra and so generalize the results of Waldenfels.

Lie Algebras and their corresponding linear groups

Mullineux involution and twisted affine Lie algebras

We use Naito-Sagaki’s work [S. Naito & D. Sagaki, J. Algebra 245 (2001) 395–412, J. Algebra 251 (2002) 461–474] on LakshmibaiSeshadri paths fixed by diagram automorphisms to study the partitions fixed by Mullineux involution. We characterize the set of Mullineux-fixed partitions in terms of crystal graph of basic representations of twisted affine Lie algebras of type A (2) 2l and of type D (2) ...

Hall basis of twisted Lie algebras

In this paper we define a minimal generating system for the free twisted Lie algebra. This gives a correct formulation and a proof to an old statement of Barratt. To this aim we use properties of the Lyndon words and of the Klyachko idempotent which generalize to twisted Hopf algebras some similar results well known in the classical case.