Recently, the authors obtained Schur multiplier, non-abelian tensor square and exterior of $d$-generator generalized Heisenberg Lie algebras rank $ \frac{1}{2}d(d-1).$ Here, we intend to obtain same results for t$ when \frac{1}{2}d(d-1)-3 \leq t\leq \frac{1}{2}d(d-1)-1.$ Then, as a result, give similar consequences nilpotent algebra L class two \dim (L/Z(L))=d,$ L^2=t such that

A two-form formulation for the N = 2 vector-tensor multiplet is constructed using superfield methods in central charge superspace. The N = 2 non-Abelian standard supergauge multiplet in central charge superspace is also discussed, as is with the associated Chern-Simons form. We give the constraints, solve the Bianchi identities and present the action for a theory of the vector-tensor multiplet ...

Erdös raised the question whether there exist infinite abelian square-free words over a given alphabet (words in which no two adjacent subwords are permutations of each other). Infinite abelian square-free words have been constructed over alphabets of sizes as small as four. In this paper, we investigate the problem of avoiding abelian squares in partial words (sequences that may contain some h...

We consider a Yang–Mills theory in loop space with an affine Lie gauge group. The Chapline–Manton coupling, the coupling between Yang–Mills fields and an abelian antisymmetric tensor field of the second rank via the Chern– Simons term, is systematically derived within the framework of the Yang–Mills theory. The generalized Chapline–Manton couplings, the couplings among nonabelian tensor fields ...

Some suucient conditions for niteness of a generalized non-abelian tensor product of groups are established extending Ellis' result for compatible actions. The non-abelian tensor product of groups was introduced by Brown and Loday 2,3] following works of A.Lue 4] and R.K.Dennis 7]. It was deened for any groups A and B which act on themselves by conjugation (x y = xyx ?1) and each of which acts ...

The notion of a tensor product of topological groups and modules is important in theory of topological groups, algebraic number theory. The tensor product of compact zero-dimensional modules over a pseudocompact algebra was introduced in [B] and for the commutative case in [GD], [L]. The notion of a tensor product of abelian groups was introduced in [H]. The tensor product of modules over commu...

Duality maps of finite abelian groups are classified. As a corollary, spin models on finite abelian groups which arise from the solutions of the modular invariance equations are determined as tensor products of indecomposable spin models. We also classify finite abelian groups whose Bose-Mesner algebra can be generated by a spin model.

A word is abelian square-free if it does not contain two adjacent subwords which are permutations of each other. Over an alphabet Σk on k letters, an abelian squarefree word is maximal if it cannot be extended to the left or right by letters from Σk and remain abelian square-free. Michael Korn proved that the length `(k) of a shortest maximal abelian square-free word satisfies 4k − 7 ≤ `(k) ≤ 6...

We investigate finitary functions from [Formula: see text] to for a square-free number text]. show that the lattice of all clones on set which contain addition is finite. provide an upper bound cardinality this through injective function direct product lattices text]-linearly closed clonoids, text], power, where These are studied in [S. Fioravanti, Closed sets between products finite fields pai...