Abstract We explored new algebra structures such as ? —algebra, —subalgebra and —ideal in this work. In addition, we study their fundamental characteristics connections with other algebras, d/?/BCK - – subalgebras ideals. Also, some examples to illustrate our notions are given. MSC (2010): 20G05, 20D06, 20B30, 20B35

The notion of bipolar fuzzy subalgebras and bipolar fuzzy ideals of a BCK/BCI-algebra is introduced, and several properties are investigated. Relations between a bipolar fuzzy subalgebra and a bipolar fuzzy ideal are given. A condition for bipolar fuzzy subalgebra to be a bipolar fuzzy ideal is provided, and the characterizations of a bipolar fuzzy ideal are stated. The concept of equivalence r...

This article is a further contribution to our research [1] into a class of infinite-dimensional Lie algebras L∞(N+, N−) generalizing the standardW∞ algebra, viewed as a tensor operator algebra of SU(1, 1) in a group-theoretic framework. Here we interpret L∞(N+, N−) either as infinite continuations of pseudo-unitary symmetries or as “higher-U(N+, N−)spin extensions” of the diffeomorphism algebra...

The purpose of this paper is to work out the categorical basis for the foundations of Conformal Field Theory. The definition of Conformal Field Theory was outlined in Segal [45] and recently given in [24] and [25]. Concepts of 2-category theory, such as versions of algebra, limit, colimit, and adjunction, are necessary for this definition. The structure present on the class C of rigged surfaces...

This article is a further contribution to our research [1] into a class of infinite-dimensional Lie algebras L∞(N+, N−) generalizing the standard W∞ algebra, viewed as a tensor operator algebra of SU(1, 1) in a group-theoretic framework. Here we interpret L∞(N+, N−) either as a infinite continuation of pseudo-unitary symmetries U(N+, N−), or as a “higher-U(N+, N−)-spin extension” of the diffeom...