In the present paper, we study notion of Schur multiplier M(L) an n-Lie superalgebra L=L0?L1 and prove that dim M(L)??i=0n(mi)L(n?i,k), where L0=m, L1=k, L(0,k)=1 L(t,k)=?j=1t(t?1j?1)(kj), for 1?t?n. Moreover, obtain upper bound dimension in which L is a nilpotent with one-dimensional derived superalgebra. It also provided several inequalities on as well analogue converse Schur’s theorem.

A criterion is given for the Lp boundedness of a class of spectral multiplier operators associated to left-invariant, homogeneous subelliptic second-order differential operators on nilpotent Lie groups, generalizing a theorem of Hörmander for radial Fourier multipliers on Euclidean space. The order of differentiability required is half the homogeneous dimension of the group, improving previous ...

We introduce a quandle invariant of classical and virtual links, denoted $Q_{tc} (L)$. This has the property that (L) \cong Q_{tc} (L')$ if only components $L$ $L'$ can be indexed in such way $L=K_1 \cup \dots K_{\mu}$, $L'=K'_1 K'_{\mu}$ for each index $i$, there is multiplier $\epsilon_i \in \{-1,1\}$ connects linking numbers over $K_i$ to $K'_i$ $L'$: $\ell_{j/i}(K_i,K_j)= \epsilon_i \ell_{j...

The paper concerns nilpotent diassociative algebras (also known as associative dialgebras) and their corresponding Schur multipliers. Using Lie (and group) theory a guide, we first extend classic five-term cohomological sequence under alternative conditions in the setting. This main result is then applied to obtain new proof for previous extension of same sequence. It also yields different that...

We demonstrate that the known off-shell nilpotent (i.e. s(a)b = 0) and anticommuting (i.e. sbsab + sabsb = 0) Becchi-Rouet-Stora-Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific cons...

Abstract The Bogomolov multiplier of a group is the unramified Brauer associated with quotient variety faithful representation group. This object an obstruction for to be stably rational. purpose this paper study these multipliers nilpotent pro-$p$ groups by transporting them their Lie algebras. Special focus set on case $p$-adic nilpotency class $2$, where we analyse moduli space. then applied...

In this paper we introduce the concept of α-commutator which its definition is based on generalized conjugate classes. With this notion, α-nilpotent groups, α-solvable groups, nilpotency and solvability of groups related to the automorphism are defined. N(G) and S(G) are the set of all nilpotency classes and the set of all solvability classes for the group G with respect to different automorphi...