The notion of a state is an analogue of a probability measure and was first introduced by Kôpka and Chovanec for MV-algebras and by Riec̆an for BLalgebras. The states have also been studied for different types of non-commutative fuzzy structures such as pseudo-MV algebras, pseudo-BL algebras, bounded R`monoids, residuated lattices and pseudo-BCK semilattices. In this paper we investigate the sta...

In this paper we give a concrete recipe how to construct triples of algebra-valued meromorphic functions on complex vector space satisfying three coupled classical dynamical Yang–Baxter equations and an associated reflection equation. Such provide the local factors consistent system first order differential operators a, generalising asymptotic boundary Knizhnik–Zamolodchikov–Bernard (KZB) equat...

Definition 1.1. Let A be an involutive algebra over C with involution ξ 7→ ξ (resp. ξ 7→ ξ). We say A is a left (resp. right) Hilbert algebra if A has a inner product (· | ·) satisfying: a. Multiplication on the left (resp. right) is a bounded operator; that is, ∀ξ ∈ A the map πl(ξ) : η 7→ ξη (resp. πr(ξ) : η 7→ ηξ) is bounded on A. b. (ξη | ζ) = (η | ξζ) (resp. (ξη | ζ) = (ξ | ζη)). c. The inv...

The notion of pseudo-valuations (valuations) on a BCC-algebra is introduced by using the Buşneag’s model ([1–3]), and a pseudo-metric is induced by a pseudo-valuation on BCC-algebras. Conditions for a real-valued function to be an BCK-pseudo-valuation are provided. The fact that the binary operation in BCC-algebras is uniformly continuous is provided based on the notion of (pseudo) valuation.

for (1), see [1], transfer the standard bracket [ , ] in sym E to the Lie algebra structures on their domain. We prove that the three new brackets are compatible. The Noether operator A0 is invertible on an open dense subset of E . This yields two recursion operators Ri = Âi ◦ A −1 0 : sym E → sym E . The images of Ri are again closed w.r.t. the commutation, and this property is retained by the...

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. A part of the so-called Gelfand–Naimark–Segal (GNS) construction is ide...

Abstract The class of pseudo-M algebras contains pseudo-BCK, pseudo-BCI, pseudo-BCH, pseudo-BE, pseudo-CI and many other logic. In this paper, the notion deductive system in a algebra is introduced its elementary properties are investigated. Closed systems defined studied. homomorphic (closed) provided. concepts translation R-congruences It shown that there bijection between closed R-congruence...

In an earlier paper we developed the classification of weakly symmetric pseudo–Riemannian manifolds $G/H$, where $G$ is a semisimple Lie group and $H$ reductive subgroup. We derived from cases compact. As consequence obtained Lorentz signature $(n-1,1)$ trans-Lorentzian $(n-2,2)$. Here work out pseudo-Riemannian nilmanifolds $G/H$ for case $G=N \rtimes H$ with compact $N$ nilpotent. It turns th...