相关论文: Projective cell modules of Frobenius cellular alge…
In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either a…
We introduce the notion of a cellular system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for an algebra to be quasi-hereditary is the existence of a full divisible cellular…
Let $G$ be a simply-connected semisimple algebraic group scheme over an algebraically closed field of characteristic $p > 0$. Let $r \geq 1$ and set $q = p^r$. We show that if a rational $G$-module $M$ is projective over the $r$-th…
In the first part of this article we prove that one of the conditions required in the original definition of nearly Frobenius algebra, the coassociativity, is redundant. Also, we determine the Frobenius dimension of the product and tensor…
We prove that applying a projective functor to a holonomic simple module over a semi-simple finite dimensional complex Lie algebra produces a module that has an essential semi-simple submodule of finite length. This implies that holonomic…
We describe a sufficient condition for the localization functor to be a categorical equivalence. Using this result we explain how to simplify the test for projectivity. This leads to a description of the strictly simple algebras which are…
An object in motivic homotopy theory is called cellular if it can be built out of motivic spheres using homotopy colimit constructions. We explore some examples and consequences of cellularity. We explain why the algebraic K-theory and…
Let $G$ be an affine algebraic group over an algebraically closed field of positive characteristic. Recent work of Hardesty, Nakano, and Sobaje gives necessary and sufficient conditions for the existence of so-called mock injective…
By means of analytic methods the quasi-projectivity of the moduli space of algebraically polarized varieties with a not necessarily reduced complex structure is proven including the case of non-uniruled polarized varieties.
A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and…
We describe the structure of projective indecomposable modules for the subalgebra consisting of the elements of degree 0 in the hyperalgebra of the $r$-th Frobenius kernel for the algebraic group ${\rm SL}_2(k)$, using the primitive…
We present a unified apoach to the study of separable and Frobenius algebras. The crucial observation is thsat both cases are related to the nonlinear equation $R^{12}R^{23}=R^{23}R^{13}=R^{13}R^{12}$, called the FS-equation. Given a…
In this note, we prove that an affine cellular algebra $A$ is semisimple if and only if the scheme associated to $A$ is reduced and 0-dimensional, and the bilinear forms with respect to all layers of $A$ are isomorphisms. Moreover, if the…
For a Frobenius cellular algebra, we prove that if the left (right) dual basis of a cellular basis is again cellular, then the algebra is symmetric. Moreover, some ideals of the center are constructed by using the so-called Nakayama twisted…
In this paper we will study the homological properties of various natural modules associated to the Fourier algebra of a locally compact group. In particular, we will focus on the question of identifying when such modules will be projective…
Over a right-noetherian algebra admitting a dualizing complex, any left-module with finite flat dimension also has finite projective dimension.
Let H be a Hopf algebra and A an H-simple right H-comodule algebra. It is shown that under certain hypotheses every (H,A)-Hopf module is either projective or free as an A-module and A is either a quasi-Frobenius or a semisimple ring. As an…
In this paper we will study the projetivity of various natural modules associated to operator Segal algebras of the Fourier algebra of a locally compact group. In particular, we will focus on the question of identifying when such modules…
Necessary and sufficient conditions are given for a $G$-graded simple module over a unital associative algebra, graded by an abelian group $G$, to be isomorphic to a loop module of a simple module, as well as for two such loop modules to be…
We study some non-semisimple representations of affine Temperley--Lieb algebras and related cellular algebras. In particular, we classify extensions between simple standard modules. Moreover, we construct a completion which is an infinite…