Opened 5 years ago
Closed 4 years ago
#23037 closed enhancement (fixed)
Implement representations for Virasoro algebra
Reported by:  tscrim  Owned by:  

Priority:  major  Milestone:  sage8.2 
Component:  algebra  Keywords:  lie algebras 
Cc:  sagecombinat, darij  Merged in:  
Authors:  Travis Scrimshaw  Reviewers:  Frédéric Chapoton 
Report Upstream:  N/A  Work issues:  
Branch:  999dcfb (Commits, GitHub, GitLab)  Commit:  999dcfba45b3b896f74aaa63f2300fde6532f7d4 
Dependencies:  Stopgaps: 
Description (last modified by )
We implement the chargeless representations and Verma modules for the Virasoro algebra. Along the way, we also add witt
to the catalog and change the bracket convention for the Witt and Virasoro algebras.
A note on the change to the bracket convention: Our current bracket convention is nonstandard with the rest of the literature and causes formulas to change in subtle ways. So the easiest thing to do is change it, and I think this will be better in the long run.
Change History (19)
comment:1 Changed 5 years ago by
 Branch set to public/lie_algebras/reprs_virasoro23037
 Commit set to 8069b1838180e4c3aac306d8ac93af1f88efb21b
 Status changed from new to needs_review
comment:2 Changed 5 years ago by
 Commit changed from 8069b1838180e4c3aac306d8ac93af1f88efb21b to aaeb1c9a7258a17d66391260ed05d299360ebfaf
Branch pushed to git repo; I updated commit sha1. New commits:
aaeb1c9  Updating documentation.

comment:3 Changed 4 years ago by
 Commit changed from aaeb1c9a7258a17d66391260ed05d299360ebfaf to 4c17c8cbaac586a2c085acf273da19e61829028f
Branch pushed to git repo; I updated commit sha1. New commits:
4c17c8c  Merge branch 'public/lie_algebras/reprs_virasoro23037' of git://trac.sagemath.org/sage into public/lie_algebras/reprs_virasoro23037

comment:4 Changed 4 years ago by
There is one it.next
that should be next(it)
for py3 sake, no ?
and doc does not build, probably because of
+ this for `\{d_i \mid 10 \leq i < 10\}::
EDIT: typo "+ REFERNCES::"
comment:5 Changed 4 years ago by
 Commit changed from 4c17c8cbaac586a2c085acf273da19e61829028f to 2fdd3e46baa3ac120646c86d0edbdc4701ad8c6f
Branch pushed to git repo; I updated commit sha1. New commits:
2fdd3e4  Use next() and typo fixes.

comment:6 Changed 4 years ago by
Yes, thanks. Fixed.
comment:7 Changed 4 years ago by
another issue here:
+ REFERENCES::
has too many colons
comment:8 Changed 4 years ago by
 Commit changed from 2fdd3e46baa3ac120646c86d0edbdc4701ad8c6f to 4b9ef9413c64d2c081977d1266b24e451d7d5aa7
Branch pushed to git repo; I updated commit sha1. New commits:
4b9ef94  No double colon on references.

comment:9 Changed 4 years ago by
Good catch. Fixed.
comment:10 Changed 4 years ago by
 Description modified (diff)
comment:11 followup: ↓ 13 Changed 4 years ago by
A strange sentence here in Verma modules:
+ The Virasoro algebra admits a triangle decomposition of
Maybe you mean of the shape
?
Otherwise, looks good.
comment:12 Changed 4 years ago by
 Commit changed from 4b9ef9413c64d2c081977d1266b24e451d7d5aa7 to 8dfb361968ed8d631bdd8f5ede5387e7fb7a1500
Branch pushed to git repo; I updated commit sha1. New commits:
8dfb361  Tweak documentation.

comment:13 in reply to: ↑ 11 Changed 4 years ago by
 Milestone changed from sage8.0 to sage8.2
Replying to chapoton:
A strange sentence here in Verma modules:
+ The Virasoro algebra admits a triangle decomposition ofMaybe you mean
of the shape
?
No, it is a triangular decomposition in the same way of simple Lie algebras or Lie groups by the root system (positive, negative, and 0 parts). I made some tweaks to the documentation; they probably don't help much, but maybe they do.
Otherwise, looks good.
Thank you very much for looking at this.
comment:14 Changed 4 years ago by
I understand the triangular decomposition, sure.
You introduced a typo : "trianglar"
I would simply remove the "of"
comment:15 Changed 4 years ago by
 Commit changed from 8dfb361968ed8d631bdd8f5ede5387e7fb7a1500 to 999dcfba45b3b896f74aaa63f2300fde6532f7d4
Branch pushed to git repo; I updated commit sha1. New commits:
999dcfb  Fixes in virasoro.VermaModule.

comment:16 Changed 4 years ago by
Ah, sorry, I misunderstood your comment:11. Here is the fix from comment:14.
comment:17 Changed 4 years ago by
 Reviewers set to Frédéric Chapoton
 Status changed from needs_review to positive_review
Thanks. Then good to go.
comment:18 Changed 4 years ago by
Thank you again very much for the review!
comment:19 Changed 4 years ago by
 Branch changed from public/lie_algebras/reprs_virasoro23037 to 999dcfba45b3b896f74aaa63f2300fde6532f7d4
 Resolution set to fixed
 Status changed from positive_review to closed
New commits:
Improving doc and check for (p)Witt algebras.
Fixed __mul__ for Lie algebra elements to handle actions.
Implement chargeless represenation.
Changing bracket convention for Witt and Virasoro. Implementing Verma modules.