bio | website | sci.ccny.cuny.edu/~benjamin |
---|---|---|
location | New York City | |
age | 42 | |
visits | member for | 4 years, 2 months |
seen | 18 mins ago | |
stats | profile views | 8,289 |
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 |
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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 |
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variance of the number of fixed points for a permutation group
r is usually called the rank of the permutation group. |
Aug
5 |
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semigroups regular!
What do you mean by a normal semigroup and finite index in this context? |
Aug
4 |
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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 |
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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 |
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Generalization of a theorem of Burnside to non-compact groups
For finite dimensional representations of discrete groups all is OK |
Jul
21 |
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Terminology for torsion semigroups where the order of elements is uniformly finite
I got this term from Rhodes |
Jul
20 |
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Terminology for torsion semigroups where the order of elements is uniformly finite
Bounded torsion is what I would say |
Jul
17 |
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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 |
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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 |
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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 |
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Maximal group image!
Since the idempotents commute in an inverse semigroup any semilattice of groups is strong. |
Jul
13 |
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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 |
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Maximal group image!
Strong semilattice of good equals clifford semigroup |
Jul
13 |
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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 |
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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 |
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Why do we need filtered categories to index ind-objects?
It's like sequences versus nets. |