We develop the covariant phase space formalism allowing for non-vanishing flux, anomalies and field dependence in vector generators. construct a charge bracket that generalizes one introduced by Barnich Troessaert includes contributions from Lagrangian its anomaly. This is uniquely determined choice of representative theory. then extend notion corner symmetry algebra to include surface translat...

We will construct the Lusztig form for the quantum loop algebra of gln by proving the conjecture [4, 3.8.6] and establish partially the Schur–Weyl duality at the integral level in this case. We will also investigate the integral form of the modified quantum affine gln by introducing an affine stabilisation property and will lift the canonical bases from affine quantum Schur algebras to a canoni...

In this paper, we enlarge the language of triangle algebra by addinga unary operation that describes properties of a state. Thesestructure algebras are called state triangle algebra. The vitalproperties of these algebras are given. The notion of state interval-valued residuated lattice (IVRL)-filters are introduced and givesome examples and properties of them are given. ...

This work concerns the study of existence and uniqueness to heat equation with fractional Laplacian dierentiation in extended Colombeau algebra.

these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...

g/u(1) d parafermions from constrained WZNW theories. Abstract The conformal field theory based on the g/u(1) d coset construction is treated as the WZNW theory for the affine Lie algebrâ g with the constrainedû(1) d subalgebra.Using a modification of the generalized canonical quantization method generators and primary fields of an extended symmetry algebra are found for arbitrary d.

We study Kuperberg invariants for sutured manifolds in the case of a semidirect product an involutory Hopf superalgebra $H$ with its automorphism group $\text{Aut}(H)$. These are topological balanced 3-manifolds endowed homomorphism fundamental into $\text{Aut}(H)$ and possibly $\text{Spin}^c$ structure homology orientation. show that these computed via form Fox calculus that, if is $\mathbb{N}...

let $f_q d_{2n}$ be the group algebra of $d_{2n}$, the dihedral group of order $2n$ over $f_q=gf(q)$. in this paper, we establish the structure of $u(f_{2^k}d_{2n})$, the unit group of $f_{2^k}d_{2n}$ and that of its normalized unitary subgroup $v_*(f_{2^k}d_{2n})$ with respect to canonical involution $*$ when $n$ is odd.