Invariant cones in solvable Lie algebras.
Displaying 41 – 60 of 102
Invariants of Lie color algebras acting on graded algebras
Jeffrey Bergen, Piotr Grzeszczuk (2000)
Colloquium Mathematicae
We prove a series of "going-up" theorems contrasting the structure of semiprime algebras and their subalgebras of invariants under the actions of Lie color algebras.
Isomorphisms and derivations in Lie -algebras.
Park, Choonkil, An, Jong Su, Cui, Jianlian (2007)
Abstract and Applied Analysis
Lie algebras of least cohomology.
Cairns, Grant, Kim, Gunky (2000)
Journal of Lie Theory
Linear maps Lie derivable at zero on 𝒥-subspace lattice algebras
Xiaofei Qi, Jinchuan Hou (2010)
Studia Mathematica
A linear map L on an algebra is said to be Lie derivable at zero if L([A,B]) = [L(A),B] + [A,L(B)] whenever [A,B] = 0. It is shown that, for a 𝒥-subspace lattice ℒ on a Banach space X satisfying dim K ≠ 2 whenever K ∈ 𝒥(ℒ), every linear map on ℱ(ℒ) (the subalgebra of all finite rank operators in the JSL algebra Alg ℒ) Lie derivable at zero is of the standard form A ↦ δ (A) + ϕ(A), where δ is a generalized derivation and ϕ is a center-valued linear map. A characterization of linear maps Lie derivable...
Local superderivations on Lie superalgebra
Haixian Chen, Ying Wang (2018)
Czechoslovak Mathematical Journal
Let be a simple strange Lie superalgebra over the complex field . In a paper by A. Ayupov, K. Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over and showed the difference between the properties of local derivations on semi-simple and nilpotent Lie algebras. We know that Lie superalgebras are a generalization of Lie algebras and the properties of some Lie superalgebras are similar to those of semi-simple Lie algebras, but is an exception. In this...
Mappings on some reflexive algebras characterized by action on zero products or Jordan zero products
Yunhe Chen, Jiankui Li (2011)
Studia Mathematica
Let 𝓛 be a subspace lattice on a Banach space X and let δ: Alg𝓛 → B(X) be a linear mapping. If ⋁ {L ∈ 𝓛 : L₋ ⊉ L}= X or ⋁ {L₋ : L ∈ 𝓛, L₋ ⊉ L} = (0), we show that the following three conditions are equivalent: (1) δ(AB) = δ(A)B + Aδ(B) whenever AB = 0; (2) δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) whenever AB + BA = 0; (3) δ is a generalized derivation and δ(I) ∈ (Alg𝓛)'. If ⋁ {L ∈ 𝓛 : L₋ ⊉ L} = X or ⋁ {L₋ : L ∈ 𝓛, L₋ ⊉ L} = (0) and δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A)...
Nonlinearity of the automorphism groups of some free algebras.
Roman'kov, V.A., Chirkov, I.V., Shevelin, M.A. (2004)
Sibirskij Matematicheskij Zhurnal
Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras
Fιndιk, Şehmus (2010)
Serdica Mathematical Journal
2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.Let Lm,c be the free m-generated metabelian nilpotent of class c Lie algebra over a field of characteristic 0. An automorphism φ of Lm,c is called normal if φ(I) = I for every ideal I of the algebra Lm,c. Such automorphisms form a normal subgroup N(Lm,c) of Aut (Lm,c) containing the group of inner automorphisms. We describe the group of normal automorphisms of Lm,c and the quotient group of Aut (Lm,c) modulo N(Lm,c).
On derivations of Lie algebras
J. de Ruiter (1974)
Compositio Mathematica
On derivations of nilpotent Lie algebras.
Barbari, P., Kobotis, A. (1998)
Balkan Journal of Geometry and its Applications (BJGA)
On nilpotent filiform Lie algebras of dimension eight.
Barbari, P., Kobotis, A. (2003)
International Journal of Mathematics and Mathematical Sciences
On quantum and classical Poisson algebras
Janusz Grabowski, Norbert Poncin (2007)
Banach Center Publications
Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular a somewhat unexpected fact that the algebras of linear differential operators acting on smooth sections of two real vector bundles of rank 1 are isomorphic as Lie algebras if and only if the base manifolds are diffeomorphic, whether or not the line bundles themselves are isomorphic....
On solvability of Lie rings with an automorphism of finite order.
Khukhro, E.I. (2001)
Sibirskij Matematicheskij Zhurnal
On the Chevalley restriction theorem.
Tevelev, E.A. (2000)
Journal of Lie Theory
On the Lie algebra of vertical prolongation operators
Josef Janyška (1982)
Czechoslovak Mathematical Journal
Orbites d'un groupe algébrique dans l'espace des idéaux rationnels d'une algèbre enveloppante
Colette Mœglin, Rudolf Rentschler (1981)
Bulletin de la Société Mathématique de France
Outer endomorphisms of free metabelian Lie algebras
Findik, Sehmus (2011)
Serdica Mathematical Journal
2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.Let Fm be the free metabelian Lie algebra of rank m over a field K of characteristic 0. We consider the semigroup IE(Fm) of the endomorphisms of Fm which are identical modulo the commutator ideal of Fm. We describe the factor semigroup of IE(Fm) modulo the congruence induced by the group of inner automorphisms.
Rational Lie Algebras and p-Isomorphisms of Nilpotent Groups and Homotopy Types.
Joseph Roitberg (1975)
Commentarii mathematici Helvetici
Skew-Symmetric Derivations of a Complex Lie Algebra.
Ignacio Bajo (1994)
Monatshefte für Mathematik