Related papers: Gel'fand-Dorfman Bialgebras
The aim of this paper is to introduce the notions of Hom Gel'fand-Dorfman bialgebra and Hom-Lie conformal algebra. In this paper, we give four constructions of Hom Gel'fand-Dorfman bialgebras. Also, we provide a general construction of…
This is a survey paper on Alegbraic Geometry over Lie Algebras
The purpose of this paper is to introduce and study super Hom-Gel'fand-Dorfman bialgebras and Hom-Lie conformal superalgebras. In this paper, we provide different ways for constructing super Hom-Gel'fand-Dorfman bialgebras and obtain some…
Gel'fand-Dorfman bialgebra, which is both a Lie algebra and a Novikov algebra with some compatibility condition, appears in the study of Hamiltonian pairs in completely integrable systems and a class of special Lie conformal algebras called…
This is a survey work on Lie algebras with ad-invariant metrics. We summarize main features, notions and constructions, in the aim of bringing into consideration the main research on the topic. We also give some list of examples in low…
This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.
Through the subsequent discussion we consider a certain particular sort of (topological) algebras, which may substitute the `` structure sheaf algebras'' in many--in point of fact, in all--the situations of a geometrical character that…
We develop a conformal analog of the theory of Poisson bialgebras as well as a bialgebra theory of Poisson conformal algebras. We introduce the notion of Poisson conformal bialgebras, which are characterized by Manin triples of Poisson…
This is a survey on coarse geometry with an emphasis on coarse homology theories.
We give a survey on Auslander-Gorenstein algebras with a focus on finite-dimensional algebras. We put an emphasis on recent classification results for special classes of algebras and the newly discovered interactions of the Auslander-Reiten…
We survey on algebraically elliptic varieties in the sense of Gromov.
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
This is a survey on stated skein algebras and their representations.
This is a survey on Kawaguchi-Silverman conjecture.
We survey a geometric approach to the Johnson homomorphisms using the Goldman-Turaev Lie bialgebra.
Gelfand--Dorfman bialgebras (GD-algebras) are nonassociative systems with two bilinear operations satisfying a series of identities that express Hamiltonian property of an operator in the formal calculus of variations. The paper is devoted…
This is an extended abstract of the talk given in the Oberwolfach miniworkshop "Nichols algebras and Weyl groupoids" in October 2012.
Novikov algebras are algebras whose associators are left-symmetric and right multiplication operators are mutually commutative. A Gel'fand-Dorfman bialgebra is a vector space with a Lie algebra structure and a Novikov algebra structure,…
In this paper we survey the main results about Golod-Shafarevich groups and their applications in algebra, number theory and topology.
This is a survey on spectral theory of dynamical systems.