Abstract
A homotopy commutative algebra, or C ∞ -algebra, is defined via the Tornike Kadeishvili homotopy transfer theorem on the vector space generated by the set of Young tableaux with self-conjugated Young diagrams \(\left \{\lambda : \lambda = \lambda ^{\prime}\right \}\). We prove that this C ∞ -algebra is generated in degree 1 by the binary and the ternary operations.
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Notes
- 1.
Strictly speaking PS(V ) is the creation parastatistics algebra, closed by creation operators alone.
- 2.
In the presence of metric one has δ : = ∂ ∗ (see below)
- 3.
The operation m 2 is associative thus the result does not depend on the choice of the bracketing.
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Acknowledgements
We are grateful to Jean-Louis Loday for many enlightening discussions and his encouraging interest. The work was supported by the French–Bulgarian Project Rila under the contract Egide-Rila N112.
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Dubois-Violette, M., Popov, T. (2013). Young Tableaux and Homotopy Commutative Algebras. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 36. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54270-4_37
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DOI: https://doi.org/10.1007/978-4-431-54270-4_37
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