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7.5.5 ncalg_lib
- Library:
- ncalg.lib
- Purpose:
- Definitions of important GR-algebras
- Authors:
- Viktor Levandovskyy, levandov@mathematik.uni-kl.de,
Oleksandr Motsak, motsak@mathematik.uni-kl.de.
- Conventions:
- This library provides pre-defined important noncommutative algebras.
For universal enveloping algebras of finite dimensional Lie algebras sl_n, gl_n and g_2 there are functions makeUsl , makeUgl and makeUg2 .
There are quantized enveloping algebras U_q(sl_2) and U_q(sl_3) (via functions makeQsl2 , makeQsl3 )
and non-standard quantum deformation of so_3, accessible via makeQso3 function.
Procedures:
7.5.5.0. makeUsl | | create U(sl_n) in char p>=0 |
7.5.5.0. makeUsl2 | | create U(sl_2) in the variables (e,f,h) in char p>=0 |
7.5.5.0. makeUg2 | | create U(g_2) in the variables (x(i),y(i),Ha,Hb) in char p>=0 |
7.5.5.0. makeUgl | | create U(gl_n) in the variables (e_ij (1<i,j<n)) in char p>=0 |
7.5.5.0. makeQso3 | | create U_q(so_3) in the presentation of Klimyk (if int n is given, the quantum parameter will be specialized at the 2n-th root of unity) |
7.5.5.0. Qso3Casimir | | returns a list with the (optionally normalized) Casimir elements of U_q(so_3) for the quantum parameter specialized at the 2n-th root of unity |
7.5.5.0. makeQsl2 | | preparation for U_q(sl_2) as factor-algebra; if n is specified, the quantum parameter q will be specialized at the n-th root of unity |
7.5.5.0. makeQsl3 | | preparation for U_q(sl_3) as factor-algebra; if n is specified, the quantum parameter q will be specialized at the n-th root of unity |
7.5.5.0. GKZsystem | | define a ring and a Gelfand-Kapranov-Zelevinsky system of differential equations |
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