Changes between Version 4 and Version 19 of Ticket #14901


Ignore:
Timestamp:
12/11/13 07:19:08 (8 years ago)
Author:
tscrim
Comment:

I've separated out Fock space into #15508. More splittings to come.

I'd also like to get Lie cohomology and connections with the exterior algebra (#15300) and De Rahm cohomology done as well.

Legend:

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  • Ticket #14901

    • Property Dependencies changed from #10963 to #10963 #14898 #15151 #15289 #15384
    • Property Branch changed from to public/algebras/lie_algebras-14901
    • Property Keywords days54 added
    • Property Commit changed from to 84b241fc071155f21f29c7169b45a6505a02bb23
    • Property Type changed from enhancement to task

  • Ticket #14901 – Description

    v4 v19  
    1111  - In the Chevalley basis
    1212- '''gl''',,n,,
    13 - The Lie algebra of strictly upper triangular matrices
    14 - The Lie algebra of upper triangular matrices
    1513- Untwisted affine Lie algebras constructed from a finite type
    1614- Untwisted affine Kac-Moody Lie algebras (i.e. the above and the Lie derivative)
    1715- Universal enveloping algebras
     16  * PBW bases
     17- Quotient, sub, and direct sum Lie algebras and Lie algebra ideals
     18- Other examples:
     19  * Upper triangular matrices
     20  * Strictly upper triangular matrices
     21  * Heisenberg algebra
     22  * Witt algebra
     23  * Virasoro algebra
     24  * Some nilpotent Lie algebras
     25- The Lyndon basis for the free Lie algebra
     26- Kac-Moody algebras based only on a (generalized) Cartan matrix
     27- Fock space #15508
    1828
    1929There might also be the following:
    2030
    21 - The Lyndon basis for the free Lie algebra
    2231- '''su''',,n,,
    23 - Kac-Moody algebras based only on a (generalized) Cartan matrix
     32- recovery of Lie group from Lie algebra
     33- connection between the quantum group and the Hall algebra (coming from representations of a quiver over Fq)
    2434
    2535With this, one will be able to do basic computations, as well as compute things such as the lower central series (depending on the type).