16,113 reputation
23797
bio website sci.ccny.cuny.edu/~benjamin
location New York City
age 42
visits member for 4 years, 2 months
seen 18 mins ago

I am an algebraist interested in a broad range of areas. I've worked on semigroups, geometric group theory, algebraic combinatorics, representation theory, self-similar groups (aka automaton groups), profinite groups and random walks on semigroups and groups. I've been particularly interested in interactions between these areas and Computer Science and am fond of algorithmic questions. I've also dabbled with operator algebras associated to etale groupoids and inverse semigroups. Currently, I am interested in applications of finite semigroup theory to finite state Markov chains.

My blog is http://bensteinberg.wordpress.com/author/bsteinbg/


Aug
20
comment Quotients of simplicial complexes which are simplicial complexes
I suspect the op wants to have the colimit agree with the one in top spaces.
Aug
17
comment variance of the number of fixed points for a permutation group
r is usually called the rank of the permutation group.
Aug
5
comment semigroups regular!
What do you mean by a normal semigroup and finite index in this context?
Aug
4
comment Which finite groups have no irreducible representations other than characters?
As @GeoffRobinson says, this is all quite well known. In ams.org/journals/tran/2009-361-03/S0002-9947-08-04712-0 we take this a step further and characterize all finite semigroups whose irreducible representations over a given field are characters. The group case is then a special case although I think we essentially reprove the group case since we need it.
Aug
4
comment Generalization of a theorem of Burnside to non-compact groups
That is the linear span of any irreducible finite dimensional representation of a group or even a semigroup is all matrices.
Aug
3
comment Generalization of a theorem of Burnside to non-compact groups
For finite dimensional representations of discrete groups all is OK
Jul
21
comment Terminology for torsion semigroups where the order of elements is uniformly finite
I got this term from Rhodes
Jul
20
comment Terminology for torsion semigroups where the order of elements is uniformly finite
Bounded torsion is what I would say
Jul
17
comment In modules over finite rings $Rv = Rw \iff R^\times v = R^\times w$
OK. I need the fact that for an artinian ring Re is isomorphic to Rf iff R(1-e) is ISO to R(1-f)
Jul
17
revised In modules over finite rings $Rv = Rw \iff R^\times v = R^\times w$
added 87 characters in body
Jul
17
comment In modules over finite rings $Rv = Rw \iff R^\times v = R^\times w$
Good point. Let me think.
Jul
17
revised In modules over finite rings $Rv = Rw \iff R^\times v = R^\times w$
added 5 characters in body
Jul
17
answered In modules over finite rings $Rv = Rw \iff R^\times v = R^\times w$
Jul
14
comment Maximal group image!
If e is a minimal idempotent then eS is the maximal subgroup and s maps to es is a retraction to S.
Jul
14
comment Maximal group image!
Since the idempotents commute in an inverse semigroup any semilattice of groups is strong.
Jul
13
comment Maximal group image!
you don't need a reference. In a semilattice the image of a word depends only on its set of letters.
Jul
13
comment Maximal group image!
Strong semilattice of good equals clifford semigroup
Jul
13
comment Maximal group image!
Alternatively, the maximal group image of a clifford inverse semigroup is the direct limit of the maximal subgroups (viewed as a directed system of groups indexed by the idempotents). In the finitely generated case the semilattice is finite so the system has a minimal element which is then the direct limit.
Jul
13
comment Maximal group image!
And multiplication by that minimal idempotent, which is central, is a homomorphism to the maximal subgroup at that idempotent which is easily checked to be the maximal group image.
Jul
10
comment Why do we need filtered categories to index ind-objects?
It's like sequences versus nets.