Related papers: Relative modular classes of Lie algebroids
We briefly review our results on the Lie theory underlying vector bundles over Lie groupoids and Lie algebroids, pointing out the role of Poisson geometry in extending these results to double Lie algebroids and LA-groupoids.
We propose a definition of Poisson quasi-Nijenhuis Lie algebroids as a natural generalization of Poisson quasi-Nijenhuis manifolds and show that any such Lie algebroid has an associated quasi-Lie bialgebroid. Therefore, also an associated…
Motivated by the universal obstruction to the deformation quantization of Poisson structures in infinite dimensions we introduce the notion of quantizable odd Lie bialgebra. The main result of the paper is a construction of a highly…
We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…
We study the moduli space of four dimensional ordinary Lie algebras, and their versal deformations. Their classification is well known; our focus in this paper is on the deformations, which yield a picture of how the moduli space is…
This paper explores the properties of multiplicative Lie algebra structures on a nilpotent group of class $2$. We also present a method for determining a multiplicative Lie algebra structure on a group that serves as an extension of one Lie…
In our earlier article [Lett. Math. Phys. 107 (2017), 475-503, arXiv:1409.8188], we explicitly described a topological Hopf algebroid playing the role of the noncommutative phase space of Lie algebra type. Ping Xu has shown that every…
We study so called regular Lie algebras, i.e. Lie algebras in which each nonzero element is regular. We make a connection with an open problem whether any element of reduced trace zero in a simple associative algebra is a commutator.
In this paper, we introduce an algebra structure denoted by InvDer algebra whose which we twist an algebra thanks to an invertible derivation, where its inverse is also a derivation. We define InvDer Lie algebras, InvDer associated…
We consider the Clifford algebra and the Clifford group associated with any quadratic module, degenerate or not, over an arbitrary commutative ring with 1. We determine some of the important subalgebras of the Clifford algebra under some…
Since 2020, finite weight modules have been studied over twisted affine Lie superalgebras. To complete the characterization of modules over affine Lie superalgebras, we need some information regarding modules over untwisted affine Lie…
In this note, we prove that intrinsic characteristic classes of Lie algebroids - which in degree one recover the modular class - behave functorially with respect to arbitrary transverse maps, and in particular are weak Morita invariants. In…
We discuss the construction of oscillator-like systems associated with orthogonal polynomials on the example of the Fibonacci oscillator. In addition, we consider the dimension of the corresponding lie algebras.
Classical r-matrices of the three-dimensional real Lie bialgebras are obtained. In this way all three-dimensional real coboundary Lie bialgebras and their types (triangular, quasitriangular or factorizable) are classified. Then, by using…
A relation between $\frac{1}{2}$-derivations of Lie algebras and transposed Poisson algebras was established. Some non-trivial transposed Poisson algebras with a certain Lie algebra (Witt algebra, algebra $\mathcal{W}(a,-1)$, thin Lie…
This article will discussing on $\frac{1}{2}$-derivations of quasi-filiform Lie algebras of maximum length. The non-trivial transposed Poisson algebras with the quasi-filiform Lie algebras of maximum length are constructed by using…
We classify the 6-dimensional Lie algebras that can be endowed with an abelian complex structure and parameterize, on each of these algebras, the space of such structures up to holomorphic isomorphism.
We determine all the contractions within the class of finite-dimensional real Lie algebras whose coadjoint orbits have dimensions $\le2$.
In this paper we define Courant algebroids in a purely algebraic way and study their deformation theory by using two different but equivalent graded Poisson algebras of degree -2. First steps towards a quantization of Courant algebroids are…
We study certain Z_2-graded, finite-dimensional polynomial algebras of degree 2 which are a special class of deformations of Lie superalgebras, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the…