In this paper we propose to find the best constant for the Friedrichs-KnappStein inequality in F2n,2, that is the free nilpotent Lie group of step two on 2n generators, and to prove the second order differentiability of subelliptic p-harmonic functions in an interval of p.

where g±d 6= 0. The positive integer d is called the depth of this Z-grading, and of the nilpotent element e. This notion was previously studied e.g. in [P1]. An element of g of the form e+ F , where F is a non-zero element of g−d, is called a cyclic element, associated with e. In [K1] Kostant proved that any cyclic element, associated with a principal (= regular) nilpotent element e, is regula...

In this paper, we define hedge operation on a residuated skew lattice and investigate some its properties. We get relationships between some special sets as dense, nilpotent, idempotent, regular elements sets and their hedges.  By examples, we show that hedge of a dense element is not a dense and hedge of a regular element is not a regular. Also hedge of a nilpotent element is a nilpotent and h...

Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $exp(G)$ and let $m=lfloorlog_pk floor$. We show that $exp(M^{(c)}(G))$ divides $exp(G)p^{m(k-1)}$, for all $cgeq1$, where $M^{(c)}(G)$ denotes the c-nilpotent multiplier of $G$. This implies that $exp( M(G))$ divides $exp(G)$, for all finite $p$-groups of class at most $p-1$. Moreover, we show that our result is an improvement...

Let $G$ be a simple algebraic group over an algebraically closed field $k$ of characteristic $p$. The classification the conjugacy classes unipotent elements $G(k)$ and nilpotent orbits on $\operatorname{Lie}(G)$ is well-established. One knows there are representatives every class as product root orbit sum elements. We give explicit in terms Chevalley basis for eminent classes. A (resp. nilpote...

Munn [11] proved that the Jacobson radical of a commutative semigroup ring is nil provided that the radical of the coefficient ring is nil. This was generalized, for semigroup algebras satisfying polynomial identities, by Okniński [14] (cf. [15, Chapter 21]), and for semigroup rings of commutative semigroups with Noetherian rings of coefficients, by Jespers [4]. It would be interesting to obtai...

Suppose GR is the real points of a complex connected reductive algebraic group G defined over R. (The class of such groups is exactly the class treated by the software package atlas.) Write g R for the dual of the Lie algebra of GR and N R for the nilpotent elements in gR. Then GR acts with finitely many orbits on N via the coadjoint action, and it is clearly very desirable to parametrize these...

Let F be either ℝ or a finite extension of ℚ p , and let G central the group F-points reductive defined over F. Also π smooth representation (Fréchet moderate growth if F=ℝ). For each nilpotent orbit

Mal’cev showed in the 1950s that there is a correspondence between radicable torsion-free nilpotent groups and rational nilpotent Lie algebras. In this paper we show how to establish the connection between the radicable hull of a finitely generated torsion-free nilpotent group and its corresponding Lie algebra algorithmically. We apply it to fast multiplication of elements of polycyclically pre...