Related papers: Self-distributive algebras and bialgebras
In this paper we introduce and study a variety of algebras that properly includes integral distributive commutative residuated lattices and weak Heyting algebras. Our main goal is to give a characterization of the principal congruences in…
A constructive approach to differential calculus on quantum principal bundles is presented. The calculus on the bundle is built in an intrinsic manner, starting from given graded (differential) *-algebras representing horizontal forms on…
The paper presents a detailed description of duality for braided algebras, coalgebras, bialgebras, Hopf algebras and their modules and comodules in the infinite setting. Assuming that the dual objects exist, it is shown how a given braiding…
We introduce and study the category of Hodge microsheaves which is a Hodge-version of the category of microsheaves for a certain class of holomorphic exact symplectic manifolds. We then study Hodge-theoretic version of wrapped sheaves and…
We introduce and investigate a natural family of metrics on connected components of a rack. The metrics are closely related to certain bi-invariant metrics on the group of inner automorphisms of the rack. We also introduce a bounded…
Bihom-associative algebras have been recently introduced in the study of group hom-categories. In this paper, we introduce a Hochschild type cohomology for bihom-associative algebras with suitable coefficients. The underlying cochain…
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…
Nichols algebras naturally appear in the classification of finite dimensional pointed Hopf algebras. Assuming only that the base field has characteristic zero several new finite dimensional rank 2 Nichols algebras of diagonal type are…
Trialitarian automorphisms are related to automorphisms of order 3 of the Dynkin diagram of type D4. Octic etale algebras with trivial discriminant, containing quartic subalgebras, are classified by Galois cohomology with value in the Weyl…
Conformal algebras, recently introduced by Kac, encode an axiomatic description of the singular part of the operator product expansion in conformal field theory. The objective of this paper is to develop the theory of ``multi-dimensional''…
We show that semisimple Hopf algebras having a self-dual faithful irreducible comodule of dimension 2 are always obtained as abelian extensions with quotient Z_2. We prove that nontrivial Hopf algebras arising in this way can be regarded as…
We study dualities between Lie algebras and Lie coalgebras, and their respective (co)representations. To allow a study of dualities in an infinite-dimensional setting, we introduce the notions of Lie monads and Lie comonads, as special…
We construct from coassociative coalgebras, bialgebras, Hopf algebras, new objects such as Poisson algebras, Leibniz algebras defined by J-L Loday and M. Ronco and explore the notion of coassociative manifolds.
We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a field of characteristic zero. We split our construction in…
Notions of self-dual and anti self-dual almost quaternionic structures are introduced. The complete classification of self-dual and anti self-dual generalized Kaehler manifolds is obtained.
A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more…
The purpose of this paper is to study twistings of Poisson algebras or bialgebras, coPoisson algebras or bialgebras and star-products. We con- sider Hom-algebraic structures generalizing classical algebraic structures by twisting the…
Principal comodule algebras can be thought of as objects representing principal bundles in non-commutative geometry. A crucial component of a principal comodule algebra is a strong connection map. For some applications it suffices to prove…
Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article…
Using the braided version of Lawvere's algebraic theories and Mac Lane's PROPs, we introduce polynomial identities for arbitrary algebraic structures in a braided monoidal category C as well as their codimensions in the case when C is…