15,457 reputation
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bio website sci.ccny.cuny.edu/~benjamin
location New York City
age 42
visits member for 3 years, 9 months
seen 3 hours 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/


2d
comment Differences between primitive central idempotents and primitive orthogonal idempotents
Yes it is. ......
Mar
25
comment Number of trivializations of a trivial word in the free group
I suspect I misunderstood what you had wanted. I some how thought you wanted to count the number of trivializations of elements of length 2n rather than the number of elements of length 2n with exactly m trivializations.
Mar
25
comment Differences between primitive central idempotents and primitive orthogonal idempotents
I think what the OP wants is that a complete set of orthogonal primitive idempotents for the center of A gives a decomposition of A into indecomposable two-sided ideals (i.e. gives a decomposition of A into indecomposable A-A bimodules).
Mar
24
comment Uninteresting questions with interesting answers
My point is to disagree with the question being uninteresting. I think the question of which diophantine problems have solutions goes back to the earliest days of mathematics and is as natural as any mathematical problem I can imagine and I am not a number theorist. So I really don't think the problem was uninteresting until the answer was known.
Mar
24
comment Uninteresting questions with interesting answers
I would say that the problem is interesting and natural. Hilbert almost surely thought there would be an algorithm and was undoubtedly aware that many natural algorithmic problems are naturally (as opposed to the Halting problem) diophantine problems.
Mar
24
comment Which way for reading the proofs?
I flagged to make CW since there is clearly no one correct answer.
Mar
23
comment Number of trivializations of a trivial word in the free group
I think Richard Stanley's enumerative combinatorics volume 2 has it. There is also the Sedgwick-Flajolet book on analytic combinatorics. A more technical book is Salomaa's book on formal power series in formal language theory (there is a coauthor but I forget who).
Mar
23
comment What are the applications of operator algebras to other areas?
I would suspect that Gelfands duality between unital commutative C*-algebras and compact Hausdorff spaces had some influence on the definition of an affine scheme.
Mar
23
comment Number of trivializations of a trivial word in the free group
You should be able to write an ambiguous context-free grammar for the type of trivialization you define and use the Chomsky -Schutzenberger method to get an algebraic generating function
Mar
22
comment Goldie's Theorem for Semigroups
I think John Fountain and his students put a lot of effort into proving as good a semigroup analogue of Goldie's theorem as possible. You might contact him.
Mar
22
comment What are the applications of operator algebras to other areas?
Isn't the Bost-Connes system supposed to tell us about the Riemann-Zeta?
Mar
19
comment What is the name for the subring of the Grothendieck ring of a bialgebra spanned by one-dimensional representations?
I think you are thinking of the case where you have a tower of algebras like symmetric group algebras and you first tensor and then induce to get a product on the direct sum of Grothendieck groups. Here I have no subalgebra to induce from.
Mar
18
asked What is the name for the subring of the Grothendieck ring of a bialgebra spanned by one-dimensional representations?
Mar
17
awarded  Nice Answer
Mar
17
comment What interesting things do automorphism groups of trees act on?
There is a measure preserving action on the space of ends with respect to product of uniform measures. This gives a unitary representation on Hilbert space
Mar
16
comment About the second largest adjacency eigenvalue of Abelian Cayley graphs
You should probably add that the group is abelian in the body of the question and not just in the title.
Mar
13
comment Brandt's definition of groupoids (1926)
Mark Lawson's inverse semigroup book also mentions the work of Brandt. Nowadays people value these things Brandt inverse semigroups.
Mar
13
comment Brandt's definition of groupoids (1926)
Eilenberg and Mac Lane in any event thought the big contribution of their paper was introducing natural transformations as the name of their paper suggests.
Mar
13
comment Brandt's definition of groupoids (1926)
Brandt's work is well known to everyone who works in semigroup theory and is discussed in the ~1967 book on semigroups by Clifford and Preston. It is not surprising that groupoids appears before categories since the fundamental groupoid has essentially been there since Poincaré
Mar
10
comment Decision problem on triviality of intersection of two subgroups
Isn't this what my added statement says except that I didn't emphasize that one of the subgroups is fixed?