We construct two associative algebras from a vertex operator algebra V and a general automorphism g of V . The first, called g-twisted zero-mode algebra, is a subquotient of what we call g-twisted universal enveloping algebra of V . These algebras are generalizations of the corresponding algebras introduced and studied by FrenkelZhu and Nagatomo-Tsuchiya in the (untwisted) case that g is the id...

In this contribution, I explain the general principles of twisted modules for vertex operator algebras in its powerful formulation using formal series, and derive new general relations satisfied by twisted and non-twisted vertex operators. I prove new “equivalence” and “construction” theorems, identifying a very restricted set of sufficient conditions in order to have a twisted module for a ver...

Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of twisted torus links and related generalizations. We determine upper bounds on their hyperbolic volumes that depend only on the number of strands being twisted. W...

Twisted cubes, crossed cubes, Möbius cubes, and locally twisted cubes are some of the widely studied hypercube variants. The 4-pancyclicity of twisted cubes, crossed cubes, Möbius cubes, locally twisted cubes and the 4-edgepancyclicity of crossed cubes are proven in [2, 1, 5, 10, 6] respectively. It should be noted that 4-edge-pancyclicity implies 4-node-pancyclicity which further implies 4-pan...

Toda equations associated with twisted loop groups are considered. Such equations are specified by Z-gradations of the corresponding twisted loop Lie algebras. The classification of Toda equations related to twisted loop Lie algebras with integrable Z-gradations is discussed.

One purpose of this paper is to define the twisted q-Bernoulli numbers by using p-adic invariant integrals on Zp. Finally, we construct the twisted q-zeta function and q-L-series which interpolate the twisted q-Bernoulli numbers.

In this paper, we introduce a family of indecomposable finitedimensional graded modules for the twisted current algebras. These modules are indexed by an |R+|-tuple of partitions ξ = (ξ)α∈R+ satisfying a natural compatibility condition. We give three equivalent presentations of these modules and show that for a particular choice of ξ these modules become isomorphic to Demazure modules in variou...

Twisted homomorphisms of bialgebras are bialgebra homomorphisms from the first into Drinfeld twistings of the second. They possess a composition operation extending composition of bialgebra homomorphisms. Gauge transformations of twists, compatible with adjacent homomorphisms, give rise to gauge transformation of twisted homomorphisms, which behave nicely with respect to compositions. Here we s...

We construct an explicit set of generators for the finite W -algebras associated to nilpotent matrices in the symplectic or orthogonal Lie algebras whose Jordan blocks are all of the same size. We use these generators to show that such finite W -algebras are quotients of twisted Yangians.