16,088 reputation
23797
bio website sci.ccny.cuny.edu/~benjamin
location New York City
age 42
visits member for 4 years, 1 month
seen 1 hour 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/


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 of the Clifford semigroup?
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 of the Clifford semigroup?
Since the idempotents commute in an inverse semigroup any semilattice of groups is strong.
Jul
13
comment Maximal group image of the Clifford semigroup?
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 of the Clifford semigroup?
Strong semilattice of good equals clifford semigroup
Jul
13
comment Maximal group image of the Clifford semigroup?
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 of the Clifford semigroup?
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.
Jul
2
comment binomial/factorial identity mod p
If p^a divides M, this is easy. Just let C_M be the cyclic group of order M and let G be the p^a element subgroup. Then G acts on the p^a element subsets if C_M and the fixed points of G are its cosets. So it follows from the fact that the number of fixed points of a p-group acting on a set is congruent to the size of the set mod p. I don't know if this idea can be adapted to the general case.
Jul
1
comment What are a couple of examples of finite sized but interesting categories?
If Q is a finite acyclic directed graph (called a quiver in this context) then the free category on Q (with vertex set the same as Q and arrows directed paths) is an interesting finite category. Functors from this category into the category of vector spaces is the same things as a quiver representation.
Jun
25
comment Independence of inverse system to define continuous cohomology for profinite groups
Presumably this is what the op means.
Jun
25
comment Independence of inverse system to define continuous cohomology for profinite groups
This definition is usually shown equivalent to the various other ones in most books like Wilson's book or Ribes and Zalesski
Jun
24
awarded  Good Answer
Jun
23
comment Next steps on formal proof of classification of finite simple groups
This seems the ideal project for computerized proofs. It is a highly cited result that many people take as a black box and which one gets the impressions has skeptics. I am not sure that a computer proof will help the true skeptics but probably some people will sleep slightly better at night knowing that there are both human and computer proofs (I just hope a computer proof wouldn't dissuade people from continuing the revision of the human proof).