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Representations of étale Lie groupoids and modules over Hopf algebroids

Jure Kališnik (2011)

Czechoslovak Mathematical Journal

The classical Serre-Swan's theorem defines an equivalence between the category of vector bundles and the category of finitely generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend these results to obtain a correspondence between the category of representations of an étale Lie groupoid and the category of modules over its Hopf algebroid that are of finite type and of constant rank. Both of these constructions are functorially...

Representation-tame incidence algebras of finite posets

Zbigniew Leszczyński (2003)

Colloquium Mathematicae

Continuing the paper [Le], we give criteria for the incidence algebra of an arbitrary finite partially ordered set to be of tame representation type. This completes our result in [Le], concerning completely separating incidence algebras of posets.

Representation-tame locally hereditary algebras

Zbigniew Leszczyński (2004)

Colloquium Mathematicae

Let A be a finite-dimensional algebra over an algebraically closed field. The algebra A is called locally hereditary if any local left ideal of A is projective. We give criteria, in terms of the Tits quadratic form, for a locally hereditary algebra to be of tame representation type. Moreover, the description of all representation-tame locally hereditary algebras is completed.

Resolutions of homogeneous bundles on ℙ 2

Giorgio Ottaviani, Elena Rubei (2005)

Annales de l’institut Fourier

We characterize minimal free resolutions of homogeneous bundles on ℙ 2 . Besides we study stability and simplicity of homogeneous bundles on ℙ 2 by means of their minimal free resolutions; in particular we give a criterion to see when a homogeneous bundle is simple by means of its minimal resolution in the case the first bundle of the resolution is irreducible.

Restricted Boolean group rings

Dinesh Udar, R.K. Sharma, J.B. Srivastava (2017)

Archivum Mathematicum

In this paper we study restricted Boolean rings and group rings. A ring R is 𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑𝐵𝑜𝑜𝑙𝑒𝑎𝑛 if every proper homomorphic image of R is boolean. Our main aim is to characterize restricted Boolean group rings. A complete characterization of non-prime restricted Boolean group rings has been obtained. Also in case of prime group rings necessary conditions have been obtained for a group ring to be restricted Boolean. A counterexample is given to show that these conditions are not sufficient.

Right coideal subalgebras of U q + ( 𝔰𝔬 2 n + 1 )

V. K. Kharchenko (2011)

Journal of the European Mathematical Society

We give a complete classification of right coideal subalgebras that contain all grouplike elements for the quantum group U q + ( 𝔰𝔬 2 n + 1 ) provided that q is not a root of 1. If q has a finite multiplicative order t > 4 ; this classification remains valid for homogeneous right coideal subalgebras of the Frobenius–Lusztig kernel u q + ( 𝔰𝔬 2 n + 1 ) . In particular, the total number of right coideal subalgebras that contain the coradical equals ( 2 n ) ! ! ; the order of the Weyl group defined by the root system of type B n .

Currently displaying 101 – 120 of 170