Related papers: A Fej\'{e}r theorem for boundary quotients arising…
We show that compatible systems of $\ell$-adic sheaves on a scheme of finite type over the ring of integers of a local field are compatible along the boundary up to stratification. This extends a theorem of Deligne on curves over a finite…
In this paper we prove several theorems about the behavior of index of Lie algebras derived from associative algebras under tensor products of underlying associative algebras.
We consider the four dimensional abelian topological BF theory with a planar boundary introduced following the Symanzik's method. We find the most general boundary conditions compatible with the fields equations broken by the boundary. The…
For systems of evolutionary partial differential equations the tau-structure is an important notion which originated from the deep relation between integrable systems and quantum field theories. We show that, under a certain non-degeneracy…
It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of strongly continuous quantum dynamical semigroups on C* algebras; this generalises the construction of…
Consider a semi-algebraic set A in R^d constructed from the sets which are determined by inequalities p_i(x)>0, p_i(x)\ge 0, or p_i(x)=0 for a given list of polynomials p_1,...,p_m. We prove several statements that fit into the following…
We compute explicitly the K-groups of some boundary groupoid C*-algebras with exponential isotropy subgroups. Then we derive index formulas that computes the K-theoretic and Fredholm indexes of elliptic (respectively totally elliptic)…
The standard C*-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does…
We analyze the Carroll-Field-Jackiw (CFJ) modification of electrodynamics reformulated as the ordinary Maxwell theory with an additional special axion field. In this form, the CFJ model appears as a special case of the pre-metric approach…
A geometrical formulation of estimation theory for finite-dimensional $C^{\star}$-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the…
Let a and b be algebraic numbers such that exactly one of a and b is an algebraic integer, and let f_t(z):=z^2+t be a family of polynomials parametrized by t. We prove that the set of all algebraic numbers t for which there exist positive…
The paper presents a criterion for a C*-algebra to be a coefficient algebra associated with a given endomorphism
In this paper, we consider the indefinite fractional elliptic problem. A corresponding Liouville-type theorem for the indefinite fractional elliptic equations is established. Furthermore, we obtain a priori bound for solutions in a bounded…
Starting from involutive BE algebras, we redefine the orthomodular algebras, by introducing the notion of implicative-orthomodular algebras. We investigate properties of implicative-orthomodular algebras, and give characterizations of these…
We study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries. Phase boundaries are instances of a more general notion of boundaries that give rise to a variety of algebraic structures. These…
Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…
Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an…
New classes of integrable boundary conditions for the q-deformed (or two-parameter) supersymmetric U model are presented. The boundary systems are solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are…
Determining when a finite dimensional algebra satisfies the finiteness property known as the $(\textbf{Fg})$-condition is of fundamental importance in the celebrated and influential theory of support varieties. We give an answer to this…
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be…