bibkey: murphy1990calgebras authors: Gerard J. Murphy year: 1990 title: C*-Algebras and Operator Theory doi: 10.1016/C2009-0-22289-6 claim: Full complex matrix algebras are simple noncommutative C*-algebras and have no characters above dimension one. strata_touched:

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C*-Algebras and Operator Theory

Gerard J. Murphy’s text develops full matrix algebras as the basic finite-dimensional noncommutative C*-algebras, together with the standard ideal and character theory that rules out a unital complex-algebra character on M_n(C) for n > 1. The repository proves the n = 2 instance directly from the anticommuting Pauli generators.

The formal declaration does not prove the arbitrary-n theorem. It is also strictly stronger in its algebraic preservation laws than a valuation on projections, so it is not presented as a Kochen-Specker result.

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• 2026-07-17: Queried NyxID/Tavily for "C*-Algebras and Operator Theory" Murphy DOI. Publisher and bibliographic records verified Gerard J. Murphy, the 1990 title, and DOI 10.1016/C2009-0-22289-6.
• 2026-07-17: Queried Murphy full matrix algebra simple characters M_n C C*-algebra. Results located the book’s standard finite-dimensional matrix algebra and character context. The repository proof was independently checked from Pauli anticommutation rather than inferred from snippets.
• 2026-07-17: Queried M2 C unital algebra homomorphism to C no character. Results agreed with the elementary simplicity/commutator obstruction; the exact Lean statement remains deliberately limited to M_2(C).

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• DOI: https://doi.org/10.1016/C2009-0-22289-6