Related papers: Centers of quantum-Wajsberg algebras
Starting from involutive BE algebras, we redefine the pre-MV and meta-MV algebras, by introducing the notion of pre-Wajsberg and meta-Wajsberg algebras, as generalizations of quantum-Wajsberg algebras. We characterize these algebras, we…
Based on implicative involutive BE algebras, we redefine the orthomodular lattices, by introducing the notion of implicative-orthomodular lattices, and we study their properties. We characterize these algebras, proving that the…
Starting from involutive BE algebras, we redefine the quantum-MV algebras, by introducing and studying the notion of quantum-Wajsberg algebras. We define the $\vee$-commutative quantum-Wajsberg algebras and we investigate their properties.…
We show that one can formulate an algebra with lattice ordering so as to contain one quantum and five classical operations as opposed to the standard formulation of the Hilbert space subspace algebra. The standard orthomodular lattice is…
We use the Jucys-Murphy elements of the BMW algebra to show that its center over the complex numbers for almost all parameters making it semisimple is given by Wheel Laurent polynomials, a subalgebra of the symmetric Laurent polynomials in…
We define and study the notions of q-deductive systems, p-deductive systems, deductive systems, maximal and strongly maximal q-deductive systems in quantum-Wajsberg algebras. We also introduce the notion of congruences induced by deductive…
Quasi-set theory was proposed as a mathematical context to investigate collections of indistinguishable objects. After presenting an outline of this theory, we define an algebra that has most of the standard properties of an orthocomplete…
Every atomic JBW-algebra is known to be a direct sum of JBW-algebra factors of type I. Extending Kadison's anti-lattice theorem, we show that each of these factors is a disjointness free anti-lattice. We characterise disjointness, bands,…
In 1978 Kostant suggested the Whittaker model of the center of the universal enveloping algebra U(g) of a complex simple Lie algebra g. The main result is that the center of U(g) is isomorphic to a commutative subalgebra in U(b), where b is…
Sachs showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as…
We give integral presentations of quantum lattice Heisenberg algebras by viewing them as Heisenberg doubles. Our presentations generalize those appearing previously in the literature.
In this paper we begin to study the subalgebra lattice of a Leibniz algebra. In particular, we deal with Leibniz algebras whose subalgebra lattice is modular, upper semi-modular, lower semi-modular, distributive, or dually atomistic. The…
The center of a semisimple Lie algebra can be described as the algebra of W-invariant functions on the dual of the Cartan subalgebra. The centers of many Lie superalgebras have a similar description, but the defining equivalence relation on…
Inspired by Aomoto's $q$-Selberg integral, the orthogonal ensemble in the exponential lattice is considered in this paper. By introducing a skew symmetric kernel, the configuration space of this ensemble is constructed to be symmetric and…
Let $L$ be a complete orthomodular lattice. There is a one to one correspondence between complete boolean subalgebras of $L$ contained in the center of $L$ and endomorphisms $j$ of $L$ satisfying the Borceux-Van den Bossche conditions.
We introduce the quasi-partition algebra $QP_k(n)$ as a centralizer algebra of the symmetric group. This algebra is a subalgebra of the partition algebra and inherits many similar combinatorial properties. We construct a basis for…
We introduce the notion of distributivity for implicative-orthomodular lattices, proving an analogue result of the Foulis-Holland theorem. Based on this result, we characterize the distributive implicative-orthomodular lattices. Moreover,…
For simply-laced quivers, we consider the fixed-point subalgebra of the quiver Hecke algebra under the homogeneous sign map. This leads to a new family of algebras we call alternating quiver Hecke algebras. We give a basis theorem and a…
In this paper, we introduce the concept of a (lattice) skew Hilbert algebra as a natural generalization of Hilbert algebras. This notion allows a unified treatment of several structures of prominent importance for mathematical logic, e.g.…
In this paper we investigate the endomorphism algebras of standard cluster tilting objects in the stably 2-Calabi-Yau categories $\Sub{\Lambda_w}$ with elements $w$ in Coxeter groups in \cite{BIRSc}. They are examples of the 2-Auslander…