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2
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1answer
45 views

Best texts on supermathematics for a mathematician?

I'm an undergraduate who's doing some summer mathematics research, and it looks like I need some information on Berezenians and supermatrices as well as supermathematics in general. The only text I ...
0
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0answers
12 views

An empirical correspondence in algebra

In the article Simplicity of Jordan superalgebras and relations with Lie structures by C. Martinez, the author states: "What is know about Jordan superalgebras with non-semisimple even part? Here the ...
0
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1answer
18 views

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 ...
1
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0answers
15 views

Finite dimensional, irreducible representations of the Lie superalgebra gl(1|1)

I am wondering how the finite dimensional, irreducible representations of the Lie superalgebra gl(1|1) are parametrized. I understand that they are all highest weight, and that the only non-trivial ...
0
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1answer
28 views

When are minimal faithful modules over algebras unique?

Let $A$ be a unital associative algebra over $\mathbb{C}$. We say an $A$-module $V$ is "minimal faithful" if (i) $V$ is faithful and (ii) $V$ does not have a proper submodule that is faithful. First ...
2
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0answers
43 views

Classical notions on super Riemann surfaces

A super Riemann surface $M$ is a complex supermanifold of dimension 1|1 with a superconformal structure given locally by an odd vector field ...
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0answers
28 views

Examples of Supergroups: U(n | m), SU(N, n|m) and PSU(N, n|m).

Looking for explicit forms of group elements in the supergroups: (1) U(n | m), (2) SU(N, n|m), (3) PSU(N, n|m), (4) PSL(n|m), (5) OSp(n|m). We can simply take $N=2$, $n=1$ and $m=1$. Partial ...
1
vote
1answer
53 views

The exterior algebra is a superalgebra?

Can someone explain how the exterior algebra of a vector space or a module over a commutative ring is a superalgebra? The exterior algebra has an obvious $\mathbb{Z}$-grading, but I don't see ...
0
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1answer
42 views

Sign convention for derivatives in a $\mathbb{Z}_2$ graded space

Suppose $V=V_0\oplus\theta V_1$ is a $\mathbb{Z}_2$ graded super vector space. Note: Since $\theta^2=0$, this implies $\theta\mathrm{d}\theta=-\mathrm{d}\theta\cdot\theta$. However, I wish to know ...
3
votes
1answer
178 views

Geometric interpretation of Supersymmetry

Is there a geometric interpretation of supersymmetry? I.e., if one has a manifold $\mathcal {M} $, and there are $\mathcal {N} $ SUSY generators, then is there a geometric interpretation of the SUSY ...
5
votes
0answers
132 views

A good reference for learning about super-differentiation & super-integration?

I've looked at a couple of books for basic information for super-differentiation & super-integration - Rogers Supermanifolds, and Khrennikovs Superanalysis. Unfortunately both books lack a clear ...
2
votes
1answer
86 views

Question about the parity of the ghost number operator in BRST quantization

Given a Lie algebra $[K_i,K_j]=f_{ij}^k K_k$, and ghost fields satisfying the anticommutation relations $\{c^i,b_j\}=\delta_j^i$, the ghost number operator is then $U=c^ib_i$ (duplicate indices are ...
12
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2answers
910 views

Grassmann numbers as eigenvalues of nilpotent operators?

The following question is motivated by the construction of the fermionic path/field integral, as done for example in Altland & Simons "Condensed Matter Field Theory". Consider the vector space ...