Related papers: Remarks on cotorsion theories
In these notes, we introduce formal hom-associative deformations of the quantum planes and the universal enveloping algebras of the two-dimensional non-abelian Lie algebras. We then show that these deformations induce formal hom-Lie…
Hecke algebras are beautiful q-extensions of Coxeter groups. In this paper, we prove several results on their characters, with an emphasis on characters induced from trivial and sign representations of parabolic subalgebras. While most of…
Vogel's universality implies a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $\alpha,\beta,\gamma$, which are homogeneous coordinates of Vogel's plane. Actually this…
We give a systematic description of the cyclic cohomology theory of Hopf algebroids in terms of its associated category of modules. Then we introduce a dual cyclic homology theory by applying cyclic duality to the underlying cocyclic…
An important combinatorial result in equivariant cohomology and $K$-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points. These formulas work…
The classical multidimensional resultant can be defined as the, suitably normalized, generator of a projective elimination ideal in the ring of universal coefficients. This is the approach via the so-called inertia forms or…
The main result of this article is the fact that the currents defined by Levin give a description of the polylogarithm of an abelian scheme at the topological level. This result was a conjecture of Levin. This provides a method to explicit…
In this paper, we study homological dimensions of algebras linked by recollements of derived module categories, and establish a series of new upper bounds and relationships among their finitistic or global dimensions. This is closely…
The cuspidal cohomology groups of arithmetic groups in certain infinite dimensional Modules are computed. As a result we get a simultaneous generalization of the Patterson-Conjecture and the Lewis-Correspondence.
Algebraic theories, sometimes called equational theories, are syntactic notions given by finitary operations and equations, such as monoids, groups, and rings. There is a well-known category-theoretic treatment of them that algebraic…
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
We consider a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, derive general scaling equation for the model, and analyse the connection between its particular forms…
We study the enumerative geometry of algebraic curves on abelian surfaces and threefolds. In the abelian surface case, the theory is parallel to the well-developed study of the reduced Gromov-Witten theory of K3 surfaces. We prove complete…
This article develops several main results for a general theory of homological algebra in categories such as the category of sheaves of idempotent modules over a topos. In the analogy with the development of homological algebra for abelian…
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
A method to construct both classical and quantum completely integrable systems from (Jordan-Lie) comodule algebras is introduced. Several integrable models based on a so(2,1) comodule algebra, two non-standard Schrodinger comodule algebras,…
The cohomology of the affine flag variety of a complex reductive group is a comodule over the cohomology of the affine Grassmannian. We give positive formulae for the coproduct of an affine Schubert class in terms of affine Stanley classes…
We study Tate-Vogel and relative cohomologies of complexes by applying the model structure induced by a complete hereditary cotorsion pair ($\A$, $\B$) of modules. We show first that the class of complexes admitting a complete $\A$…
In this paper we show that certain universal homology classes which are fundamental in topology are algebraic. To be specific, the products of Eilenberg-MacLane spaces ${\cal K}_{2q} \equiv K({\Bbb Z},2) \times K({\Bbb Z}, 4) \times ...…
Loop quantum gravity corrections, in the presence of inhomogeneities, can lead to a deformed constraint algebra. Such a deformation implies that the effective theory is no longer generally covariant. As a consequence, the geometrical…