Related papers: Coding theory applied to KU-algebras
Clifford geometric algebras of multivectors are introduced which exhibit a bilinear form which is not necessarily symmetric. Looking at a subset of bi-vectors in CL(K^{2n},B), we proof that theses elements generate the Hecke algebra…
We develop a diagrammatic categorification of the polynomial ring Z[x], based on a geometrically defined graded algebra. This construction generalizes to categorification of some special functions, such as Chebyshev polynomials.…
We define generalized bialgebras and Hopf algebras and on this basis we introduce quantum categories and quantum groupoids. The quantization of the category of linear (super)spaces is constructed. We establish a criterion for the classical…
We develop the K-theory of sets with an action of a pointed monoid (or monoid scheme), analogous to the $K$-theory of modules over a ring (or scheme). In order to form localization sequences, we construct the quotient category of a nice…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
The paper "Sorting with Bialgebras and Distributive Laws" by Hinze et al. uses the framework of bialgebraic semantics to define sorting algorithms. From distributive laws between functors they construct pairs of sorting algorithms using…
We develop deformation theory of algebras over quadratic operads where the parameter space is a commutative local algebra. We also give a construction of a distinguised deformation of an algebra over a quadratic operad with a complete local…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
We survey recent generalizations and improvements of the linear programming method that involve semidefinite programming. A general framework using group representations and tools from graph theory is provided.
We prove that "unitary deformation K-theory" takes products of finitely generated groups to coproducts of algebra spectra over ku, the connective K-theory spectrum. Additionally, we give spectral sequences for computing the homotopy groups…
We introduce quantum Boolean algebras which are the analogue of the Weyl algebras for Boolean affine spaces. We study quantum Boolean algebras from the logical and set theoretical viewpoints.
Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…
We deduce from a determinant identity on quantum transfer matrices of generalized quantum integrable spin chain model their generating functions. We construct the isomorphism of Clifford algebra modules of sequences of transfer matrices and…
We introduce a generating function associated to the homogeneous generators of a graded algebra that measures how far is this algebra from being finitely generated. For the case of some algebras of Frobenius endomorphisms we describe this…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
We define a general notion of set of indices which, using concepts from pre-ordered sets theory, permits to unify the presentation of several Colombeau-type algebras of nonlinear generalized functions. In every set of indices it is possible…
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
We compute the K-theory for C*-algebras naturally associated with rings of integers in number fields. The main ingredient is a duality theorem for arbitrary global fields. It allows us to identify the crossed product arising from affine…
We define a notion of formal quantum field theory and associate a formal quantum field theory to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfaces. This enables us to find an effective way to compute…