In this paper we generalize Drinfeld's twisted quantum affine algebras to construct twisted quantum algebras for all simply-laced generalized Cartan matrices and present their vertex representation realizations.2010 Mathematics Subject Classification. 17B37, 17B10.

Let g be an affine Kac-Moody algebra, and µ a diagram automorphism of g. In this paper, we give an explicit realization for the universal central extension g[µ] of the twisted loop algebra of g related to µ, which provides a Moody-Rao-Yokonuma presentation for the algebra g[µ] when µ is nontransitive, and the presentation is indeed related to the quantization of toroidal Lie algebras. √ −1/N . In this paper, we study the universal central extension g[µ] of L(ḡ,μ), and give Moody-Rao-Yokonuma presentation for g [µ] when µ is non-transitive. One may expect that the MRY 2010 Mathematics Subject Classification. 17B67.

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This is a continuation of a previous study initiated by one of us on nonlocal vertex bialgebras and smash product nonlocal vertex algebras. In this paper, we study a notion of right H-comodule nonlocal vertex algebra for a nonlocal vertex bialgebra H and give a construction of deformations of vertex algebras with a right H-comodule nonlocal vertex algebra structure and a compatible H-module nonlocal vertex algebra structure. We also give a construction of φ-coordinated quasi modules for smash product nonlocal vertex algebras. As an example, we give a family of quantum vertex algebras by deforming the vertex algebras associated to non-degenerate even lattices.