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Description: |
In this talk we will give in detail an inductive description of odd-quadratic Lie superalgebras
such that the even part is a reductive Lie algebra. We will present the construction of odd double extension of
an odd-quadratic Lie superalgebras by the one-dimensional Lie algebra
and generalized odd double extension of an odd-quadratic Lie superalgebra by the one-dimensional Lie
superalgebra with even part zero. After that we will analyse the
particular case of odd-quadratic Lie superalgebras such that the
even part is a reductive Lie algebra. Contrarily to quadratic case,
for odd-quadratic Lie superalgebra such that the even part is a
reductive Lie algebra the action of the even part on the odd part is
completely reducible. We will prove that a non-zero odd-quadratic Lie superalgebra of our
type is either an algebra of Gell-Mann, Michel and Radicati $ d(n)/{ KI_{2n}}$,
($n \geq 3$), or obtained from a finite number of element of
the former part by a finite sequence of generalized odd double
extensions by the one-dimensional Lie superalgebra, and/or by
trivial odd double extensions of simple Lie algebra, and/or by
orthogonal direct sums. Finally, we will prove that a quadratic Lie
superalgebra with the even part a reductive Lie algebra, with
certain conditions, does not admit an odd-invariant scalar product,
and vice versa.
Area(s):
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Date: |
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| Start Time: |
14:30 |
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Speaker: |
Elisabete Barreiro (Dep. de Matemática, FCTUC)
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Place: |
5.5
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| Research Groups: |
-Geometry
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See more:
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<Main>
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