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135
The ramification of centres: Lie algebras in positive characteristic and quantised enveloping algebras
 Math. Z
, 2001
"... ar ..."
Problems in the Steenrod algebra
 Bull. London Math. Soc
, 1998
"... This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may find of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development ..."
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Cited by 30 (1 self)
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This article contains a collection of results and problems about the Steenrod algebra and related algebras acting on polynomials which nonspecialists in topology may find of some interest. Although there are topological allusions throughout the article, the emphasis is on the algebraic development of the Steenrod algebra and its connections to the various topics indicated below. Contents 1 Historical background 4
characteristics as invariants of Iwasawa modules
 Proc. London Math. Soc
, 2002
"... Let G be a prop, padic, Lie group with no element of order p and let Λ(G) denote the Iwasawa algebra of G, defined in the usual way by ..."
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Cited by 23 (0 self)
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Let G be a prop, padic, Lie group with no element of order p and let Λ(G) denote the Iwasawa algebra of G, defined in the usual way by
Foxby equivalence over associative rings
"... Abstract. We extend the definition of a semidualizing module to associative rings. This enables us to define and study Auslander and Bass classes with respect to a semidualizing bimodule C. We then study the classes of Cflats, Cprojectives, and Cinjectives, and use them to provide a characterizat ..."
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Cited by 19 (5 self)
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Abstract. We extend the definition of a semidualizing module to associative rings. This enables us to define and study Auslander and Bass classes with respect to a semidualizing bimodule C. We then study the classes of Cflats, Cprojectives, and Cinjectives, and use them to provide a characterization of the modules in the Auslander and Bass classes. We extend Foxby equivalence to this new setting. This paper contains a few results which are new in the commutative, noetherian setting.
Quantum Teichmüller space as a noncommutative algebraic object
, 2008
"... We consider the quantum Teichmüller space of the punctured surface introduced by ChekhovFockKashaev, and formalize it as a noncommutative deformation of the space of algebraic functions on the Teichmüller space of the surface. In order to apply it in 3dimensional topology, we put more attention ..."
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Cited by 15 (4 self)
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We consider the quantum Teichmüller space of the punctured surface introduced by ChekhovFockKashaev, and formalize it as a noncommutative deformation of the space of algebraic functions on the Teichmüller space of the surface. In order to apply it in 3dimensional topology, we put more attention to the details involving small surfaces.
Prime regular Hopf algebras of GKdimension one
"... Abstract. This paper constitutes the first part of a program to classify all affine prime regular Hopf algebras H of GelfandKirillov dimension one over an algebraically closed field of characteristic zero. We prove a number of properties of such an algebra, list some classes of examples, and then p ..."
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Cited by 12 (8 self)
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Abstract. This paper constitutes the first part of a program to classify all affine prime regular Hopf algebras H of GelfandKirillov dimension one over an algebraically closed field of characteristic zero. We prove a number of properties of such an algebra, list some classes of examples, and then prove that when the PIdegree of H is prime our list contains all such algebras. 0.1. Recent years have seen substantial progress in our understanding of (infinite dimensional) noetherian Hopf algebras [BG1, LWZ, WZ1, BZ]. One noteworthy aspect of this development has been the increasing role of homological algebra for example, it was shown in [WZ1] that every affine noetherian Hopf algebra satisfying
Representation Theory Of Noetherian Hopf Algebras Satisfying A Polynomial Identity
, 1997
"... . A class of Noetherian Hopf algebras satisfying a polynomial identity is axiomatised and studied. This class includes group algebras of abelianbyfinite groups, finite dimensional restricted Lie algebras, and quantised enveloping algebras and quantised function algebras at roots of unity. Some ..."
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Cited by 11 (4 self)
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. A class of Noetherian Hopf algebras satisfying a polynomial identity is axiomatised and studied. This class includes group algebras of abelianbyfinite groups, finite dimensional restricted Lie algebras, and quantised enveloping algebras and quantised function algebras at roots of unity. Some common homological and representationtheoretic features of these algebras are described, with some indications of recent and current developments in research on each of the exemplar classes. It is shown that the finite dimensional representation theory of each of these algebras H reduces to the study of a collection Alg(H) of (finite dimensional) Frobenius algebras. The properties of this family of finite dimensional algebras are shown to be intimately connected with geometrical features of central subHopf algebras of H. A number of open questions are listed throughout. 1. Introduction My aim in this paper is to review some common properties exhibited by four large and important cla...
Examples of generic noncommutative surfaces
, 2002
"... We study a class of noncommutative surfaces and their higher dimensional analogues which provide answers to several open questions in noncommutative projective geometry. Specifically, we give the first known graded algebras which are noetherian but not strongly noetherian, answering a question of A ..."
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Cited by 9 (2 self)
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We study a class of noncommutative surfaces and their higher dimensional analogues which provide answers to several open questions in noncommutative projective geometry. Specifically, we give the first known graded algebras which are noetherian but not strongly noetherian, answering a question of Artin, Small, and Zhang. In addition, these examples are maximal orders and satisfy the χ1 condition but not χi for i ≥ 2, answering a questions of Stafford and Zhang and a question of Stafford and Van den Bergh. Finally, we show that