Search results for "JOINT"
showing 10 items of 1472 documents
Some criteria for detecting capable Lie algebras
2013
Abstract In virtue of a recent bound obtained in [P. Niroomand, F.G. Russo, A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra 39 (2011) 1293–1297], we classify all capable nilpotent Lie algebras of finite dimension possessing a derived subalgebra of dimension one. Indirectly, we find also a criterion for detecting noncapable Lie algebras. The final part contains a construction, which shows that there exist capable Lie algebras of arbitrary big corank (in the sense of Berkovich–Zhou).
Lie nilpotence of group rings
1993
Let FG be the group algebra of a group G over a field F. Denote by ∗ the natural involution, (∑fi gi -1. Let S and K denote the set of symmetric and skew symmetric and skew symmetric elements respectively with respect to this involutin. It is proved that if the characteristic of F is zero p≠2 and G has no 2-elements, then the Lie nilpotence of S or K implies the Lie nilpotence of FG.
A restriction on the schur multiplier of nilpotent lie algebras
2011
An improvement of a bound of Yankosky (2003) is presented in this paper, thanks to a restriction which has been recently obtained by the authors on the Schur multiplier M(L) of a finite dimensional nilpotent Lie algebra L. It is also described the structure of all nilpotent Lie algebras such that the bound is attained. An important role is played by the presence of a derived subalgebra of maximal dimension. This allows precision on the size of M(L). Among other results, applications to the non-abelian tensor square L ⊗ L are illustrated.
Group algebras of torsion groups and Lie nilpotence
2010
Letbe an involution of a group algebra FG induced by an involution of the group G. For char F 0 2, we classify the torsion groups G with no elements of order 2 whose Lie al- gebra of � -skew elements is nilpotent.
Non-self-adjoint resolutions of the identity and associated operators
2013
Closed operators in Hilbert space defined by a non-self-adjoint resolution of the identity $$\{X(\lambda )\}_{\lambda \in {\mathbb R}}$$ , whose adjoints constitute also a resolution of the identity, are studied. In particular, it is shown that a closed operator $$B$$ has a spectral representation analogous to the familiar one for self-adjoint operators if and only if $$B=\textit{TAT}^{-1}$$ where $$A$$ is self-adjoint and $$T$$ is a bounded inverse.
Nilpotent Lie algebras with 2-dimensional commutator ideals
2011
Abstract We classify all (finitely dimensional) nilpotent Lie k -algebras h with 2-dimensional commutator ideals h ′ , extending a known result to the case where h ′ is non-central and k is an arbitrary field. It turns out that, while the structure of h depends on the field k if h ′ is central, it is independent of k if h ′ is non-central and is uniquely determined by the dimension of h . In the case where k is algebraically or real closed, we also list all nilpotent Lie k -algebras h with 2-dimensional central commutator ideals h ′ and dim k h ⩽ 11 .
A note on strongly Lie nilpotency
1991
In this note the authors studies strongly Lie nilpotent rings and proves that if a ringR is strongly Lie nilpotent thenR(2), the ideal generated by all commutators, is nilpotent.
Associative rings with metabelian adjoint group
2004
Abstract The set of all elements of an associative ring R, not necessarily with a unit element, forms a monoid under the circle operation r∘s=r+s+rs on R whose group of all invertible elements is called the adjoint group of R and denoted by R°. The ring R is radical if R=R°. It is proved that a radical ring R is Lie metabelian if and only if its adjoint group R° is metabelian. This yields a positive answer to a question raised by S. Jennings and repeated later by A. Krasil'nikov. Furthermore, for a ring R with unity whose multiplicative group R ∗ is metabelian, it is shown that R is Lie metabelian, provided that R is generated by R ∗ and R modulo its Jacobson radical is commutative and arti…
Radical Rings with Engel Conditions
2000
Abstract An associative ring R without unity is called radical if it coincides with its Jacobson radical, which means that the set of all elements of R forms a group denoted by R ∘ under the circle operation r ∘ s = r + s + rs on R . It is proved that, for a radical ring R , the group R ∘ satisfies an n -Engel condition for some positive integer n if and only if R is m -Engel as a Lie ring for some positive integer m depending only on n .
Metric operators, generalized hermiticity and partial inner product spaces
2015
A quasi-Hermitian operator is an operator in a Hilbert space that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure of metric operators, bounded or unbounded, in a Hilbert space. We introduce several generalizations of the notion of similarity between operators and explore to what extent they preserve spectral properties. Next we consider canonical lattices of Hilbert spaces generated by unbounded metric operators. Since such lattices constitute the simplest case of a partial inner product space (PIP space), we can exploit the te…