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On Constant-Trace Representations of Degenerate Clifford Algebras

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Abstract

In this paper, we complement some recent results of L. Márki, J. Meyer, J. Szigeti and L. van Wyk, by investigating the constant-trace representations of a Clifford algebra \(C(V)\) of an arbitrary quadratic form \(q:V\rightarrow F\) (possibly degenerate) and we present some relevant applications. In particular, the existence of the polynomial identities of \(C(V)\) of particular form when the characteristic of the base field is zero is looked at. Furthermore, a lower bound is found on the minimal number t, such that \(C(V)\) can be embedded in a matrix ring of degree t, over some commutative F-algebra. Also, some results on the dimension of commutative subalgebras of \(C(V)\) are obtained.

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Acknowledgements

The authors would like to express their sincere gratitude to the referees for careful reading of this paper and for their constructive comments and judicious suggestions leading to the improvement of the final form of this manuscript. Further, H. H. Sidhwa would like to thank Sharif University of Technology for the hospitality which the university provided to the author during his stay for postdoctoral work.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Sharif University of Technology, P. O. Box 11155-9415, Tehran, Iran

    M. G. Mahmoudi & H. H. Sidhwa

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  1. M. G. Mahmoudi
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  2. H. H. Sidhwa
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Correspondence to H. H. Sidhwa.

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Communicated by Michaela Vancliff

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Mahmoudi, M.G., Sidhwa, H.H. On Constant-Trace Representations of Degenerate Clifford Algebras. Adv. Appl. Clifford Algebras 31, 52 (2021). https://doi.org/10.1007/s00006-021-01150-7

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