Timeline for What is growth of ass. algebra with 3 generators and relation a1a2a3 + a2a3a1 +a3a1a2 - a1a3a2 - a2a1a3 -a3a2a1 ?
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| Nov 21, 2011 at 14:46 | comment | added | David E Speyer | Thanks for the reference! Anick's paper looks very definitive. | |
| Nov 21, 2011 at 12:39 | comment | added | Vladimir Dotsenko | Oh, and for your last question: it is used in an awful lot of places, from deformation theory to theoretical computer science. Since the publication of Anick's paper in 1986, quite a few people rediscovered his results in various contexts! | |
| Nov 21, 2011 at 12:08 | comment | added | Vladimir Dotsenko | Spans are over the ground field $k$, as well as tensor products (because of this we can compute Euler characteristics). The right $B$-module on $V\otimes B$ is via the action on $B$ alone: $(v\otimes b)b':=v\otimes(bb')$. Of course it works for any number of $a_i$'s, and the construction I use is a very special case of a construction due to David Anick (ams.org/mathscinet-getitem?mr=846601). | |
| Nov 21, 2011 at 12:05 | history | edited | Vladimir Dotsenko | CC BY-SA 3.0 |
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| Nov 21, 2011 at 11:55 | comment | added | Alexander Chervov | @Volodya Thank You ! But I not quite get: span - means what ? Algebra or module ? spanned from the left or from the both sides over B or over all algebra ? Tensor product - as algebras over C or as C vector spaces ? Why this is right modules than ? This probably works for any number of a_i - does it have some name ? where is it used ? | |
| Nov 21, 2011 at 10:29 | history | answered | Vladimir Dotsenko | CC BY-SA 3.0 |