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In spite of the provocative title this is a run of the mill review of supersymmetry. The only thing which deserves some comment is that the author seems to think that coordinate free and coordinate dependent treatments belong to conflicting cultures. This is definitely not true. Coordinate free treatments concentrate one's mind on the geometry while coordinate dependent treatments are indispensable for computations producing numbers which can be compared with experimental values. Those who use the...

Supersymmetry algebras: extensions of orthgonal Lie algebras

Hasiewicz, Zbigniew (1987)

Proceedings of the 14th Winter School on Abstract Analysis

Symmetric algebras and Yang-Baxter equation

Beidar, K., Fong, Y., Stolin, A. (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

Let $U$ be an open subset of the complex plane, and let $L$ denote a finite-dimensional complex simple Lie algebra. A. A. Belavin and V. G. Drinfel’d investigated non-degenerate meromorphic functions from $U \times U$ into $L \otimes L$ which are solutions of the classical Yang-Baxter equation [Funct. Anal. Appl. 16, 159-180 (1983; Zbl 0504.22016)]. They found that (up to equivalence) the solutions depend only on the difference of the two variables and that their set of poles forms a discrete (additive) subgroup $Γ$ of the...

Symmetrization of brace algebra

Daily, Marilyn, Lada, Tom (2006)

Proceedings of the 25th Winter School "Geometry and Physics"

Summary: We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra. We also show that the symmetrization of the natural brace structure on $⨁_{k \geq 1} Hom (V^{\otimes k}, V)$ coincides with the natural symmetric brace structure on $⨁_{k \geq 1} Hom {(V^{\otimes k}, V)}^{a s}$ , the direct sum of spaces of antisymmetric maps $V^{\otimes k} \to V$ .

Symplectic solution supermanifolds in field theory

Schmitt, T. (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

Summary: For a large class of classical field models used for realistic quantum field theoretic models, an infinite-dimensional supermanifold of classical solutions in Minkowski space can be constructed. This solution supermanifold carries a natural symplectic structure; the resulting Poisson brackets between the field strengths are the classical prototypes of the canonical (anti-) commutation relations. Moreover, we discuss symmetries and the Noether theorem in this context.

Systems of covers of frames and resulting subframes

Kříž, I., Pultr, A. (1987)

Proceedings of the 14th Winter School on Abstract Analysis

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