Urrutia, L. F.; Morales, N. An extension of the Cayley-Hamilton theorem to the case of supermatrices. (English) Zbl 0816.15027 Lett. Math. Phys. 32, No. 3, 211-219 (1994). There appears to be nothing new in this paper that has not already been reported by the authors [J. Phys. A 26, L441–L447 (1993; Zbl 0777.15006)] and [J. Phys. A 27, 1981-1997 (1994)]. Reviewer: N.Backhouse (Liverpool) Cited in 1 Review MSC: 15A75 Exterior algebra, Grassmann algebras 15A90 Applications of matrix theory to physics (MSC2000) 81T60 Supersymmetric field theories in quantum mechanics 83E99 Unified, higher-dimensional and super field theories Keywords:Grassmann algebra; Cayley-Hamilton theorem; supermatrix Citations:Zbl 0777.15006 PDFBibTeX XMLCite \textit{L. F. Urrutia} and \textit{N. Morales}, Lett. Math. Phys. 32, No. 3, 211--219 (1994; Zbl 0816.15027) Full Text: DOI arXiv References: [1] For a review see, for example, Birmingham, D., Blau, M., Rakowski, M. and Thompson, G.,Phys. Rep. 209, 129 (1991). [2] Jones, V.,Bull. AMS 12, 103 (1985) andPacific J. Math. 137, 312 (1989); Freyd, P., Yetter, D., Hoste, J., Lickorish, W., Millet, K., and Ocneanu, A.,Bull. AMS 12, 239 (1985); Kauffman, L.,Topology 26, 395 (1987); Witten, E.,Comm. Math. Phys. 121, 351 (1989) andNuclear Phys. B322, 629 (1989). · Zbl 0564.57006 [3] Witten, E.,Nuclear Phys. B311, 46 (1988/89). [4] Horne, J. H.,Nuclear Phys. B334, 669 (1990). [5] Nelson, J. E., Regge, T., and Zertuche, F.,Nuclear Phys. B339 516, (1990). [6] Koehler, K., Mansouri, F., Vaz, C., and Witten, L.,Modern Phys. Lett. A5, 935 (1990);Nuclear Phys. B341, 167 (1990) andNuclear Phys. B348, 373 (1991). · Zbl 1020.83685 [7] Urrutia, L. F., Waelbroeck, H., and Zertuche, F.,Modern Phys. Lett. A7, 2715 (1992). · Zbl 1021.81926 [8] Mandelstam, S.,Phys. Rev. D, 2391 (1979). [9] Berenstein, D. E. and Urrutia, L. F.,J. Math. Phys. 35, 1922 (1994). · Zbl 0802.15005 [10] For a review see, for example, Loll., R.,Teor. Mat. Fiz. 93, 481 (1992) and Preprint Pennsylvania State University CGPG-93/9-1, September 1993; Brügmann, B., Preprint Max Planck Institute of Physics, MPI-Ph/93-94, December 1993. [11] For a discussion of this point see, for example, Henneaux, M. and Teitelboim, C.,Quantization of Gauge Systems, Princeton University Press, New Jersey, 1993, Chapter 6. [12] See, for example, De Witt, B.,Supermanifolds, Cambridge University Press, Cambridge, 1984. [13] Backhouse, N. B. and Fellouris, A. G.,J. Phys. A17, 1389 (1984). [14] Kobayashi, Y. and Nagamachi, S.,J. Math. Phys. 31, 2726 (1990). · Zbl 0725.15025 [15] See, for example, Nering, E. D.,Linear Algebra and Matrix Theory, 2nd edn, Wiley, New York, 1970. [16] Urrutia, L. F. and Morales, N.,J. Phys. A26, L441 (1993); Urrutia, L. F., The relation between the Mandelstam and Cayley-Hamilton identities: their extension to the case of supermatrices, to appear in P. Letelier,et al. (eds),Proceedings of SILARG-8, World Scientific, Singapore; Urrutia, L. F. and Morales, N., The Cayley-Hamilton theorem for supermatrices, in N. Bretón, R. Capovilla and T. Matos, (eds),Proc. Aspects of General Relativity and Mathematical Physics, dedicated to the 65th birthday of Jerzy Plebanky, p. 162. · Zbl 0777.15006 [17] Urrutia, L. F. and Morales, N.,J. Phys. A 27, 1981 (1994). · Zbl 0834.15026 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.