Archivio Istituzionale della RicercaWe generalize the classical isomorphism between symmetric functions and invariants of a matrix. In particular we show that the invariants over several matrices are given by a the abelianization of the symmetric tensors over the free associative algebra. The main result is proved by finding a characteristic free presentation of the algebra of symmetric tensors over a free algebra.
Generalized symmetric functions and invariants of matrices, / Vaccarino, Francesco. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 260:(2008), pp. 509-526. [10.1007/s00209-007-0285-2]
Generalized symmetric functions and invariants of matrices,
VACCARINO, FRANCESCO
2008
Abstract
We generalize the classical isomorphism between symmetric functions and invariants of a matrix. In particular we show that the invariants over several matrices are given by a the abelianization of the symmetric tensors over the free associative algebra. The main result is proved by finding a characteristic free presentation of the algebra of symmetric tensors over a free algebra.
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https://hdl.handle.net/11583/1646141
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