#16837: Lie superalgebras
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Reporter: bransingh | Owner:
Type: task | Status: new
Priority: major | Milestone: sage-wishlist
Component: algebra | Resolution:
Keywords: Lie superalgebras | Merged in:
Authors: Biswajit Ransingh,.. | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by bransingh):
'''This is just a rough way of computing Lie superbracket'''
Definition: F.super_bracket(self, x, y)
Source:
def super_bracket(self, x, y):
"""
Returns the Lie super bracket `[x, y] = x y -(-1)^{|x||y|} y
x` of `x` and `y`.
INPUT:
- ``x``, ``y`` -- elements of ``self``
EXAMPLES::
sage: F = SuperAlgebrasWithBasis(QQ).example()
sage: F
An example of an superalgebra with basis: the free
superalgebra on the generators ('a', 'b', 'c') over Rational Field
sage: a,b,c = F.super_algebra_generators()
sage: F.super_bracket(a,b)
B[word: ab] - B[word: ba]
This measures the default of commutation between `x` and `y`.
`F` endowed with the super_bracket operation is a Lie super
algebra;
in particular, it satisfies super Jacobi's identity::
sage: F.super_bracket( F.super_bracket(a,b), c) +
F.super_bracket(F.super_bracket(b,c),a) +
F.super_bracket(F.super_bracket(c,a),b)
0
"""
def degree(self,x):
if x is even:
0
else:
1
return x*y - (-1)^{degree(x)*degree(y)}y*x
--
Ticket URL: <http://trac.sagemath.org/ticket/16837#comment:4>
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