Questions tagged [superalgebra]

For questions about superalgebra, which is a kind of graded algebra.

In mathematics and theoretical physics, a superalgebra is a $\Bbb Z_2$-graded algebra. That is, it is an algebra over a commutative ring or field with a decomposition into "even" and "odd" pieces and a multiplication operator that respects the grading.

The prefix super- comes from the theory of supersymmetry in theoretical physics. Superalgebras and their representations, supermodules, provide an algebraic framework for formulating supersymmetry. The study of such objects is sometimes called super linear algebra. Superalgebras also play an important role in related field of supergeometry where they enter into the definitions of graded manifolds, supermanifolds and superschemes.

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How to formulate supercommutativity in a characteristic free way?

I believe I've seen an answer to this somewhere (some Deligne notes?) but cannot recover it. In the $\mathbb Z/2$-graded formulation, supercommutativity means that two odd degree elements anticommute while all other kinds of homogeneous elements…
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Grading on subspace of super vector space

Let $H=H^0\oplus H^1$ be some super vector space and $E\subseteq H$ a vector subspace. One might think that by setting $$E^k:=E\cap H^k$$ we obtain a new super vector space $E=E^0\oplus E^1$, but this is generally not the case, is it? I don't see…
Filippo
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inhomogeneous elements in vector superspace?

I am currently studying Lie Superalgebra, and having a confusion on basic concepts of superalgebra. From Kac's Lie Superalgebra(p.13), it says that "if deg$a$ appears in a given Superalgebra, then it is assumed that $a$ is homogeneous, and that the…
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How is this algebra a superalgebra?

In this set of notes http://arxiv.org/pdf/0809.1380.pdf on page ix he seems to be claiming that the algebra $\mathrm{End}(V)[[z,z^{-1}]]$ is a superalgebra (where $V$ is any vector space over $\mathbb{C}$). If it's a superalgebra, what would the…
Rupert
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