Related papers: Classification of states on certain orthomodular s…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
Let $\mathcal A$ be a unital algebra equipped with an involution $(\cdot)^\dagger$, and suppose that the multiplicative set $\mathcal S\subseteq \mathcal A$ generated by the elements of the form $1 + a^\dagger a$ satisfies the Ore…
The unital endomorphisms of B(H) of (Powers) index n are classified by certain U(n)-orbits in the set of non-degenerate representations of the Cuntz algebra O_n on H. Using this, the corre- sponding conjugacy classes are identified, and a…
We prove that Archimedean sharply dominating atomic lattice effect algebras can be characterized by property called basic decomposition of elements. As an application we prove the state smearing theorem for these effect algebras.
In this paper we show that using implicative algebras one can produce models of set theory generalizing Heyting/Boolean-valued models and realizability models of (I)ZF, both in intuitionistic and classical logic. This has as consequence…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
We explore the integration of representations from a Lie algebra to its algebraic group in positive characteristic. An integrable module is stable under the twists by group elements. Our aim is to investigate cohomological obstructions for…
Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced…
A well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not representable in the standard quantum logic, the lattice $L({\mathcal H})$ of all closed subspaces of a separable complex…
The aim of this paper is to introduce the notion of fantastic deductive systems on generalizations of fuzzy structures, and to emphasize their role in the probability theory on these algebras. We give a characterization of commutative…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
To provide tools, especially L-operators, for use in studies of rational Yang-Baxter algebras and quantum integrable models when the Lie algebras so(N) (b_n, d_n) or sp(2n) (c_n) are the invariance algebras of their R matrices, this paper…
Vertex algebras formalize the subalgebra of holomorphic fields of a conformal field theory. OPE-algebras were proposed as a generalization of vertex algebras that formalizes the algebra of all fields of a conformal field theory. We prove…
We introduce and obtain multimode paraboson coherent states. In appropriate subspaces these coherent states provide a decomposition of unity where the measure, when expressed using the cat-type states, is positive definite. Bicoherent…
Eigenvalues are defined for any element of an algebra of observables and do not require a representation in terms of wave functions or density matrices. A systematic algebraic derivation based on moments is presented here for the harmonic…
We define a state as a $[0,1]$-valued, finitely additive function attaining the value $1$ on an EMV-algebra, which is an algebraic structure close to MV-algebras, where the top element is not assumed. We show that states always exist, the…
We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…
In the paper, we define the notion of a state BCK-algebra and a state-morphism BCK-algebra extending the language of BCK-algebras by adding a unary operator which models probabilistic reasoning. We present a relation between state operators…
In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…
This article addresses the question of involutiveness and discusses the initial value problem for a class of overdetermined systems of partial differential equations which arise in the theory of integrable systems and are defined by…