Biswas, Indranil
Dey, Arijit
Poddar, Mainak
LetXbe a complete toric variety equipped with the action of a torusT, andGa reductive algebraic group, defined over an algebraically closed fieldK. We introduce the notion of a compatible n-ary sumation -filtered algebra associated toX, generalizing the notion of a compatible n-ary sumation -filtered vector space due to Klyachko, where n-ary sumation denotes the fan ofX. We combine Klyachko's classification ofT-equivariant vector bundles onXwith Nori's Tannakian approach to principalG-bundles, to give an equivalence of categories betweenT-equivariant principalG-bundles onXand certain compatible n-ary sumation -filtered algebras associated toX, when the characteristic ofKis 0.


Galois structure of modular forms of even weight
Gurel, E. (Elsevier BV, 2009-10-01)
We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
Value sets of Lattes maps over finite fields
Küçüksakallı, Ömer (Elsevier BV, 2014-10-01)
We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication.
Local left invertibility for operator tuples and noncommutative localizations
Dosiev, Anar (Cambridge University Press (CUP), 2009-01-01)
In the paper we propose an operator approach to the noncommutative Taylor localization problem based on the local left invertibility for operator tuples acting on a Frechet space. We prove that the canonical homomorphism U(g) -> O(g) of the universal enveloping algebra U(g) of a nilpotent Lie algebra g into its Arens-Michael envelope O(g) is the Taylor localization whenever g has normal growth.
On algebraic K-theory of real algebraic varieties with circle action
Ozan, Yıldıray (Elsevier BV, 2002-05-24)
Assume that X is a compact connected orientable nonsingular real algebraic variety with an algebraic free S-1-action so that the quotient Y=X/S-1 is also a real algebraic variety. If pi:X --> Y is the quotient map then the induced map between reduced algebraic K-groups, tensored with Q, pi* : (K) over bar (0)(R(Y, C)) circle times Q --> (K) over bar (0)(R(X, C)) circle times Q is onto, where R(X, C) = R(X) circle times C, R(X) denoting the ring of entire rational (regular) functions on the real algebraic va...
A technical note on weak shift equivalence
Tezer, Cem (Elsevier BV, 1999-06-01)
Weak shift equivalence which arises in the dynamical study of certain attractors is shown to be an equivalence relation among group endomorphisms. (C) 1999 Academic Press.
Citation Formats
I. Biswas, A. Dey, and M. Poddar, “TANNAKIAN CLASSIFICATION OF EQUIVARIANT PRINCIPAL BUNDLES ON TORIC VARIETIES,” TRANSFORMATION GROUPS, pp. 0–0, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/67099.