Implement fusion algebras #15485

tscrim · 2013-12-05T01:52:24Z

As defined by Fuchs for WZW field theories.

CC: @sagetrac-sage-combinat @anneschilling @darijgr @dwbump

Component: algebra

Keywords: fusion algebras, rings, quantum groups, CFT

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/15485

tscrim · 2013-12-05T02:13:51Z

New commits:

`[22fcc30](https://github.com/sagemath/sagetrac-mirror/commit/22fcc30)`	`Initial implementation.`
`[9dca526](https://github.com/sagemath/sagetrac-mirror/commit/9dca526)`	`Added comparison operations.`
`[a493bee](https://github.com/sagemath/sagetrac-mirror/commit/a493bee)`	`Merge branch 'master' into public/monoids/15289-indexed`
`[c1b5afe](https://github.com/sagemath/sagetrac-mirror/commit/c1b5afe)`	`#15289: Implemented indexed monoids and groups.`
`[6fd33b2](https://github.com/sagemath/sagetrac-mirror/commit/6fd33b2)`	`#15169: Fix FreeAlgebra element constructor from a base field.`

tscrim · 2013-12-05T02:13:51Z

Branch: public/algebras/fusion_algebras-15485

tscrim · 2013-12-05T02:13:51Z

Dependencies: #15289

tscrim · 2013-12-05T02:13:51Z

Commit: 22fcc30

sagetrac-git · 2014-02-08T17:40:14Z

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`dc50e22`	`Merge branch 'develop' into public/algebras/fusion_algebras-15485`
`6c8a02e`	`Merge branch 'develop' into public/algebras/fusion_algebras-15485`
`12f1412`	`Merge branch 'develop' into public/algebras/fusion_algebras-15485`
`c37df3e`	`Merge branch 'develop' into public/algebras/fusion_algebras-15485`
`1bcda69`	`Merge branch 'develop' into public/algebras/fusion_algebras-15485`
`545a8df`	`Merge branch 'develop' into public/monoids/15289-indexed`
`2975c87`	`Merge branch 'develop' into public/monoids/15289-indexed`
`4002b0d`	`Merge branch 'develop' into public/monoids/15289-indexed`
`9e9b769`	`Merge branch 'develop' into public/monoids/15289-indexed`
`a278afa`	`Added cardinality methods.`

sagetrac-git · 2014-02-08T17:40:14Z

Changed commit from 22fcc30 to 967207a

sagetrac-git · 2014-04-09T02:13:10Z

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`56703eb`	`Made Indexed* have entry points through Free*.`
`163df6e`	`Changed more _basis_keys to _indices, deprecated the former.`
`8db8e0a`	Changed `_an_element_` to indexed_monoid.py.
`760c939`	`Merge branch 'public/monoids/15289-indexed' of trac.sagemath.org:sage into public/monoids/15289-indexed`
`03057a4`	`Merge branch 'develop' into public/monoids/15289-indexed`
`a2996e0`	`Merge branch 'develop' into public/monoids/15289-indexed`
`c1cc341`	`Merge branch 'develop' into public/monoids/15289-indexed`
`49068b2`	`Merge branch 'develop' into public/monoids/15289-indexed`
`6875cfb`	`Merge branch 'develop' into public/monoids/15289-indexed`
`47a7f51`	`Merge branch 'public/algebras/fusion_algebras-15485' of trac.sagemath.org:sage into public/algebras/fusion_algebras-15485`

sagetrac-git · 2014-04-09T02:13:10Z

Changed commit from 967207a to 47a7f51

sagetrac-git · 2014-04-15T02:27:30Z

Branch pushed to git repo; I updated commit sha1. New commits:

`1818a3e`	`Merge branch 'develop' into public/monoids/15289-indexed`
`8b2566f`	`Merge branch 'public/monoids/15289-indexed' into public/algebras/fusion_algebras-15485`

sagetrac-git · 2014-04-15T02:27:30Z

Changed commit from 47a7f51 to 8b2566f

sagetrac-git · 2014-05-17T21:41:22Z

Changed commit from 8b2566f to 49dba22

sagetrac-git · 2014-05-17T21:41:22Z

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`18fd094`	`Fixed affine weight lattice symmetric form.`
`cb88df7`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`760194b`	`More changes and fixes.`
`eab1afe`	`Fixed doctest.`
`66f5674`	`Fixed type BC positive roots.`
`e17ce53`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`7e83910`	`Fixes for other twisted root systems.`
`c91754d`	`Merge branch 'develop' into public/combinat/root_systems/improvements-15384`
`c71ee92`	`Merge branch 'public/combinat/root_systems/improvements-15384' into public/algebras/fusion_algebras-15485`
`49dba22`	`Fixed doctests from recent versions.`

tscrim · 2014-05-17T21:41:51Z

Changed dependencies from #15289 to #15289 #15384

sagetrac-git · 2014-07-25T07:23:19Z

Changed commit from 49dba22 to 7876b6e

sagetrac-git · 2014-07-25T07:23:19Z

Branch pushed to git repo; I updated commit sha1. New commits:

`7876b6e`	`Merge branch 'public/algebras/fusion_algebras-15485' of trac.sagemath.org:sage into public/algebras/fusion_algebras-15485`

sagetrac-git · 2015-03-17T18:25:51Z

Changed commit from 7876b6e to 840c56b

sagetrac-git · 2017-10-01T00:56:31Z

Changed commit from f29afd8 to f05b087

sagetrac-git · 2017-10-01T00:56:31Z

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`f05b087`	`Improving documentation, changing FusionAlgebra -> VerlindeAlgebra, other updates.`

tscrim · 2017-10-01T01:08:07Z

comment:26

Replying to @koffie:

I thought maybe it was not to much work to learn what fusion algebras are, but this seems more work then expected. So here some non mathematical comments.

All the same, thank you for taking a look at the ticket.

in the class docstring it might be good to list the INPUT: heading before all the mathematical explanation going on (but after the only senctence description of this class). This is something you want to be able to see at a quick glance if you sort of know how to use this class but forgot what the exact input was.

I disagree with this as I feel it is better to define your objects for people. If you need to look at the inputs, it takes 3 seconds to scroll to find the INPUT: block. Also, I think Sage more consistently has things this way.

The examples in the __init__ function should be in a TESTS: section instead

This really doesn't matter, but done.

Is there a reason you don't subclass sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra.FiniteDimensionalAlgebra Otherwise, if this gives problems, you should at least make it behave more like a FiniteDimensionalAlgebra, by making a function that computes the underlying FiniteDimensionalAlgebra and delegates the most important function to the abstract underlying algebra to make it behave like a FiniteDimensionalAlgebra in order for users to have a consistent user experience.

Yes, there are many. Most importantly, it would mean we have to construct the entire multiplication table upon initialization rather than on-demand, which could be very expensive. Also, FiniteDimensionalAlgebra is a more concrete implementation than CombinatorialFreeModule and does not have the same feature set in terms of indexing of the basis. The consistency should be controlled through the category (is gen the thing you are talking about?); so if you want something, lift it from FiniteDimensionalAlgebra (or have some generic implementation or requirement added to the API).

This raises an error:
sage: F(F.monomial(0))*F(F.monomial(1))

As it should. monomial wants something of the index set (although this is not checked currently for speed reasons and Python's "consenting adults" philosophy). While 0 could be considered in the index set, 1 definitely is not.

While this works

sage: F.gens()[0] * F.gens()[1]
F[Lambda[2]]

You should not do this. See below.

It would be nice to have a method gen like FreeModule(QQ,42) has (although admittedly this is a shortcoming of CombinatorialFreeModule) I just found this out in testing this ticket.

I completely disagree because gens (and hence gen) is ambiguous, and hence, should generally be avoided. In particular, the generators as a what? See #15381 and #17768.

In this case, there is not a good way to determine what generates it as an algebra, so the generators as an R-algebra are the same as those as a free R-module. Yet, in this case, there is no natural order on the generators because there is no natural order on the indexing set.

dwbump · 2018-10-04T17:02:58Z

comment:27

The documentation in algebras/verlinde_algebra.py .mentions the "Kac-Waldron formula". I think this should be "Kac-Walton".

Walton, Mark A. Fusion rules in Wess-Zumino-Witten models. Nuclear Phys. B 340 (1990), no. 2-3, 777–790.

Also in algebras/verlinde_algebra.py [Feigngold2004] should be [Feingold2004].

sagetrac-git · 2018-10-08T00:57:41Z

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`7603245`	`Initial implementation.`
`592aa5b`	`Fixed doctests from recent versions.`
`177e074`	`trac #15485 fixing the catalog`
`2febb38`	`Improving documentation, changing FusionAlgebra -> VerlindeAlgebra, other updates.`
`4492c9d`	`Fixing various small things.`

sagetrac-git · 2018-10-08T00:57:41Z

Changed commit from f05b087 to 4492c9d

tscrim · 2018-10-08T00:59:44Z

comment:30

I have fixed Dan's comment:27 (Waldron must have been a Freudenthal slip :P). I also rebased this over the current develop to help clean up the history a bit.

fchapoton · 2021-03-26T09:06:20Z

comment:31

red branch => needs work

tscrim · 2021-03-26T23:33:26Z

Changed branch from public/algebras/fusion_algebras-15485 to none

tscrim · 2021-03-26T23:33:26Z

comment:33

This is a duplicate of #26440.

tscrim · 2021-03-26T23:33:26Z

Reviewer: Travis Scrimshaw

tscrim · 2021-03-26T23:33:26Z

Changed commit from 4492c9d to none

tscrim · 2021-03-26T23:33:26Z

Changed author from Travis Scrimshaw to none

tscrim · 2021-03-26T23:33:26Z

Changed dependencies from #15289 #15384 to none

tscrim added this to the sage-6.0 milestone Dec 5, 2013

tscrim added c: algebra labels Dec 5, 2013

tscrim assigned sagetrac-sage-combinat Dec 5, 2013

tscrim added the s: needs review label Dec 5, 2013

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.0, sage-6.1 Dec 17, 2013

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.1, sage-6.2 Jan 30, 2014

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.2, sage-6.3 May 6, 2014

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.3, sage-6.4 Aug 10, 2014

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tscrim added s: needs review and removed s: needs work labels Oct 1, 2017

fchapoton added s: needs work and removed s: needs review labels Mar 26, 2021

fchapoton modified the milestones: sage-8.1, sage-9.4 Mar 26, 2021

tscrim added s: positive review and removed s: needs work labels Mar 26, 2021

tscrim removed this from the sage-9.4 milestone Mar 26, 2021

fchapoton removed the s: positive review label Mar 27, 2021

fchapoton closed this as completed Mar 27, 2021

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tscrim mentioned this issue Jun 17, 2022

Lie algebras #14901

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dwbump mannequin mentioned this issue Oct 29, 2018

Fusion algebras from Weyl Character Rings #26440

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Implement fusion algebras #15485

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Implement fusion algebras #15485

Implement fusion algebras #15485

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