Defining relations of minimal degree of the trace algebra of 3 X 3 matrices

Francesca Saviella Benanti, Vesselin Drensky

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Abstract

The trace algebra Cnd over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n, d 2. Starting with the generating set of C3d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C3d is equal to 7 for any d 3. We have determined all relations of minimal degree. For d = 3 we have also found the defining relations of degree 8.
Lingua originaleEnglish
pagine (da-a)103-110
Numero di pagine8
RivistaCOMPTES RENDUS DE L'ACADÉMIE BULGARE DES SCIENCES
Volume60
Stato di pubblicazionePublished - 2007

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Defining Relations
Trace
Algebra
Generating Set

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abstract = "The trace algebra Cnd over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n, d 2. Starting with the generating set of C3d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C3d is equal to 7 for any d 3. We have determined all relations of minimal degree. For d = 3 we have also found the defining relations of degree 8.",
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AU - Benanti, Francesca Saviella

AU - Drensky, Vesselin

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N2 - The trace algebra Cnd over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n, d 2. Starting with the generating set of C3d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C3d is equal to 7 for any d 3. We have determined all relations of minimal degree. For d = 3 we have also found the defining relations of degree 8.

AB - The trace algebra Cnd over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n, d 2. Starting with the generating set of C3d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C3d is equal to 7 for any d 3. We have determined all relations of minimal degree. For d = 3 we have also found the defining relations of degree 8.

UR - http://hdl.handle.net/10447/9531

UR - http://www.proceedings.bas.bg/

M3 - Article

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JO - Comptes Rendus de L'Academie Bulgare des Sciences

JF - Comptes Rendus de L'Academie Bulgare des Sciences

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