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
NAME | Title | EMAIL @manchester.ac.uk | PHONE | LOCATION | |
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 |