Related papers: Poisson-Lie U-duality in Exceptional Field Theory

A thorough analysis of Lie super-bialgebra structures on Lie super-algebras osp(1|2) and super-e(2) is presented. Combined technique of computer algebraic computations and a subsequent identification of equivalent structures is applied. In…

Drinfeld classified Poisson homogeneous spaces of a Poisson Lie group in terms of Dirac structures of the Lie bialgebra. In this paper, we study homogeneous spaces of a 2-group and develop Drinfeld theorem in the Poisson 2-group context.

We study the cohomology (cocycles) of Lie superalgebras for the generalised complex of forms: superforms, pseudoforms and integral forms. We argue that these cocycles might be interpreted in the light of a new brane scan as generators of…

We study pseudoalgebras from the point of view of pseudo-dual of classical Lie coalgebra structures. We define the notions of Lie H-coalgebra and Lie pseudo-bialgebra. We obtain the analog of the CYBE, the Manin triples and Drinfeld's…

Poisson-Lie target space duality is a framework where duality transformations are properly defined. In this letter we investigate the pair of sigma models defined by the double SO(3,1) in the Iwasawa decomposition.

We construct a generalized cluster structure compatible with the Poisson bracket on the Drinfeld double of the standard Poisson-Lie group $GL_n$ and derive from it a generalized cluster structure on $GL_n$ compatible with the push-forward…

This paper is devoted to the study of Poisson superalgebras over fields of characteristic $2$. We investigate their representations, semidirect products, cohomology, formal deformations, and universal enveloping algebras. We also introduce…

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 introduce coupled double Poisson brackets on an associative algebra $A$ as pairs consisting of a generalized Van den Bergh's double Poisson bracket and a generalized Fairon--McCulloch's right double Poisson bracket subject to a…

A new non-standard deformation of all types of classical Lie algebras is constructed by means of Drinfel'd twist based on a six dimensional subalgebra. This is an extension of extended twists introduced by Kulish et al. For the algebra M_3…

We review (and elaborate on) the `dual graviton problem' in the context of duality covariant formulations of M-theory (exceptional field theories). These theories require fields that are interpreted as components of the dual graviton in…

We propose a Leibniz algebra, to be called DD$^+$, which is a generalization of the Drinfel'd double. We find that there is a one-to-one correspondence between a DD$^+$ and a Jacobi--Lie bialgebra, extending the known correspondence between…

For a particular class of backgrounds, equations of motion for string sigma models targeted in mutually dual Poisson-Lie groups are equivalent. This phenomenon is called the Poisson-Lie T-duality. On the level of the corresponding string…

E.B. Vinberg's theory of quasi-derivations of algebras is extended to a broader framework of near-derivations. This deepens connections between Poisson geometry and Lie theory. Although basic results apply to arbitrary algebras, our…

Let A_k denote the twisted group algebra of the symmetric group S_k, whose representations correspond to the nonlinear projective representations of S_k. We establish a duality relation between A_k and a Lie superalgebra q(n), sometimes…

Hidden symmetries are the backbone of Integrable two-dimensional theories. They provide classical solutions of higher dimensional models as well, they seem to survive partially quantisation and their discrete remnants in M-theory called…

We introduce the notion of $\lambda$-double Lie algebra, which coincides with usual double Lie algebra when $\lambda = 0$. We state that every $\lambda$-double Lie algebra for $\lambda\neq0$ provides the structure of modified double Poisson…

We address the issue of T-duality and U-duality symmetries in the toroidally-compactified type IIA string. It is customary to take as a starting point the dimensionally-reduced maximal supergravity theories, with certain field strengths…

We study general properties of Hodge-type decompositions of cyclic and Hochschild homology of universal enveloping algebras of (DG) Lie algebras. Our construction generalizes the operadic construction of cyclic homology of Lie algebras due…

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…