Vortex filament on symmetric Lie algebras and generalized bi-Schrödinger flows
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-017-2014-9
Abstract: In this article, we display an evolving model on symmetric Lie algebras from a purely geometric way by using the Hamiltonian (or para-Hamiltonian) gradient flow of a fourth order functional called generalized bi-Schrödinger flows, which… read more here.
Keywords: vortex filament; lie algebras; symmetric lie; schr dinger ... See more keywords
On self-similar Lie algebras and virtual endomorphisms
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-018-2146-6
Abstract: We introduce the notion of virtual endomorphisms of Lie algebras and use it as an approach for constructing self-similarity of Lie algebras. This is done in particular for a class of metabelian Lie algebras having… read more here.
Keywords: self similar; lie; virtual endomorphisms; lie algebras ... See more keywords
Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras
Sign Up to like & getrecommendations! Published in 2018 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-020-02510-y
Abstract: We prove that the tensor product of a simple and a finite dimensional $${\mathfrak {sl}}_n$$ sl n -module has finite type socle. This is applied to reduce classification of simple $${\mathfrak {q}}(n)$$ q ( n… read more here.
Keywords: algebras simple; lie algebras; simple mathfrak; translated simple ... See more keywords
Restricted Lie 2-algebras
Sign Up to like & getrecommendations! Published in 2018 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-017-7065-7
Abstract: In this article, we introduce the notions of restricted Lie 2-algebras and crossed modules of restricted Lie algebras, and give a series of examples of restricted Lie 2-algebras. We also construct restricted Lie 2-algebras from… read more here.
Keywords: restricted lie; lie algebras; algebras restricted;
Lie Algebras of Slow Growth and Klein-Gordon PDE
Sign Up to like & getrecommendations! Published in 2018 at "Algebras and Representation Theory"
DOI: 10.1007/s10468-018-9794-4
Abstract: AbstractWe discuss the notion of characteristic Lie algebra of a hyperbolic PDE. The integrability of a hyperbolic PDE is closely related to the properties of the corresponding characteristic Lie algebra χ. We establish two explicit… read more here.
Keywords: lie; lie algebras; mathfrak mathbb; pde ... See more keywords
Complete classification of pseudo H-type algebras: II
Sign Up to like & getrecommendations! Published in 2018 at "Geometriae Dedicata"
DOI: 10.1007/s10711-018-0411-9
Abstract: We classify a class of 2-step nilpotent Lie algebras related to the representations of the Clifford algebras in the following way. Let $$J:{{\mathrm{\mathrm {Cl}}}}({\mathbb {R}}^{r,s})\rightarrow {{\mathrm{End}}}(U)$$J:Cl(Rr,s)→End(U) be a representation of the Clifford algebra $${{\mathrm{\mathrm {Cl}}}}({\mathbb… read more here.
Keywords: lie algebras; classification pseudo; type algebras; pseudo type ... See more keywords
$${{\,\mathrm{{\mathfrak {L}}}\,}}$$-prolongations of graded Lie algebras
Sign Up to like & getrecommendations! Published in 2020 at "Geometriae Dedicata"
DOI: 10.1007/s10711-020-00510-0
Abstract: In this paper we translate the necessary and sufficient conditions of Tanaka’s theorem on the finiteness of effective prolongations of a fundamental graded Lie algebras into computationally effective criteria, involving the rank of some matrices… read more here.
Keywords: mathfrak prolongations; lie algebras; prolongations graded; mathrm mathfrak ... See more keywords
On the A. V. Mikhalev Problem for Weakly Artinian Lie Algebras
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-018-3949-z
Abstract: The A. V. Mikhalev problem for weakly Artinian Lie algebras is solved. The theorem about solvability of prime radical of weakly Artinian Lie algebras is proved. An analogous result was generalized for Ω-groups. read more here.
Keywords: artinian lie; lie algebras; weakly artinian; mikhalev problem ... See more keywords
On Segal–Sugawara vectors and Casimir elements for classical Lie algebras
Sign Up to like & getrecommendations! Published in 2020 at "Letters in Mathematical Physics"
DOI: 10.1007/s11005-020-01344-3
Abstract: We consider the centers of the affine vertex algebras at the critical level associated with simple Lie algebras. We derive new formulas for generators of the centers in the classical types. We also give a… read more here.
Keywords: lie; lie algebras; classical lie; sugawara vectors ... See more keywords
Lie Algebras Associated with Modules over Polynomial Rings
Sign Up to like & getrecommendations! Published in 2017 at "Ukrainian Mathematical Journal"
DOI: 10.1007/s11253-018-1442-y
Abstract: Let ???? be an algebraically closed field with characteristic zero and let V be a module over the polynomial ring ????[x, y]. The actions of x and y specify linear operators P and Q on… read more here.
Keywords: lie; lie algebras; algebras isomorphic; weakly isomorphic ... See more keywords
Twisted Forms of Differential Lie Algebras over $${\mathbb {C}}(t)$$ C ( t ) Associated with Complex Simple Lie Algebras
Sign Up to like & getrecommendations! Published in 2020 at "Arnold Mathematical Journal"
DOI: 10.1007/s40598-020-00155-7
Abstract: Discussed here is descent theory in the differential context where everything is equipped with a differential operator. To answer a question personally posed by A. Pianzola, we determine all twisted forms of the differential Lie algebras… read more here.
Keywords: differential lie; lie; lie algebras; twisted forms ... See more keywords