Abstract
The notion of an extended solution plays a key role in Uhlenbeck’s approach to the description of harmonic maps to the unitary group. In the present paper, we extend this notion to the case of a noncommutative sigma model (a quantum analog of harmonic spheres in the unitary group) and use it to establish that the minimum uniton number of any diagonal solution is equal to the canonical rank of this solution.
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References
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Original Russian Text © A.V. Domrina, 2012, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Vol. 279, pp. 72–80.
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Domrina, A.V. Extended solutions in a noncommutative sigma model. Proc. Steklov Inst. Math. 279, 64–72 (2012). https://doi.org/10.1134/S0081543812080068
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DOI: https://doi.org/10.1134/S0081543812080068