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Research in Algebra

The Algebra group plays a major role in the School's research activities. We run a weekly Algebra seminar and also organize occasional seminars of a more specialised nature. There are many interactions with other research areas in the school, notably with topology, geometry and combinatorics and mathematical logic.

Research Interests

Research interests of the algebraists at the University of Manchester include: Lie theory; representation theory; group theory; group geometries; graph theory; quantum algebra; homological algebra; homotopy theory; combinatorics; black box groups; model theory; invariant theory; structure and representation theory of algebraic groups and related Lie algebras; semigroup theory; tropical algebra; computational algebra; cohomology, modular and ordinary representation theory of finite groups; the unit group of the Steenrod algebra; representations of quivers and algebras; group actions on rings, topological spaces and free Lie algebras.

Members of staff interests

Dr Yuri Bazlov:

Hopf algebras and quantum groups, applications to representation theory, combinatorics and integrable systems.

Professor Alexandre Borovik:

Group Theory: structural properties and finite subgroups of simple algebraic groups; black box groups and non-deterministic methods; Combinatorics: discrete geometries and configurations arising from homogeneous spaces, Model Theory: groups of finite Morley rank

Professor Roger Bryant (Emeritus):

Groups acting on free Lie algebras; automorphisms of relatively free groups.

Dr Charles Eaton:

Ordinary and modular representation theory of finite groups.

Dr Marianne Johnson:

Free Lie algebras, representation theory, semigroup theory, tropical algebra and geometry.

Dr Mark Kambites:

Combinatorial and geometric group theory, semigroup theory, formal languages and automata, computational complexity, parallel processing, cryptography, and interactions between the above.

Professor Alexander Premet:

Lie Theory: classifications of finite dimensional simple Lie algebras, enveloping algebras, primitive ideas, finite W-algebras; Modular Representation Theory of Reductive Lie Algebras; Invariant Theory of Algebraic Groups.

Professor Mike Prest

The Ziegler spectrum of an associative ring, representations of algebras and quivers; structure and complexity of categories of modules and other additive categories.

Professor Peter Rowley

Finite Simple Groups, Amalgams of groups and completions of amalgams, Group Geometries, Point-Line Collinearity Graphs of Sporadic Simple Groups, Coxeter Groups, Commuting Graphs and Cages.

Professor Toby Stafford

Non-commutative algebra, non-commutative algebraic geometry, rings of differential operators

Professor Ralph Stohr

Lie Algebras: Group actions on free Lie algebras. Group Theory: Homological methods in Group Theory, Combinatorial Group Theory, Equations over groups.

Professor Peter Symonds

Representation theory and cohomology of groups, homological algebra, profinite groups, group actions on rings, group actions on topological spaces, homotopy theory, and invariant theory.

Contact details

Bazlov Yuri Dr Yuri.Bazlov 0161 27 55816 2.220
Borovik Alexandre Prof. Alexandre.Borovik 0161 30 63645 2.125
Bryant Roger Prof. (Emeritus) Roger.Bryant 0161 30 63642 1.115
Eaton Charles Dr (Royal Society Research Fellow) Charles.Eaton 0161 30 63697 2.135
Johnson Marianne Dr Marianne.Johnson 0161 27 55821 2.143
Kambites Mark Dr Mark.Kambites 0161 30 63211 2.144
Premet Alexander A Prof. A.Premet 0161 27 55854 1.131
Prest Mike Prof. MPrest 0161 27 55875 1.120
Rowley Peter Prof. Peter.Rowley 0161 30 63648 2.131
Stafford Toby Prof. Toby.Stafford 0161 27 55828 2.116
Stöhr Ralph Prof. Ralph.Stohr 0161 30 63647 2.140
Symonds Peter Prof. Peter.Symonds 0161 30 63675 2.209
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