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Mendes, S. (2026). C*-Algebras and the Noncommutative Geometry of Semifields. Workshop on Operator Theory, Complex Analysis, and Applications 2026 - WOTCA 2026.

S. M. Mendes,  "C*-Algebras and the Noncommutative Geometry of Semifields", in Workshop on Operator Theory, Complex Analysis, and Applications 2026 - WOTCA 2026, Guimarães, 2026

@misc{mendes2026_1788019483851,
	author = "Mendes, S.",
	title = "C*-Algebras and the Noncommutative Geometry of Semifields",
	year = "2026",
	howpublished = "Digital",
	url = "https://sites.google.com/view/wotca-2026"
}

TY  - CPAPER
TI  - C*-Algebras and the Noncommutative Geometry of Semifields
T2  - Workshop on Operator Theory, Complex Analysis, and Applications 2026 - WOTCA 2026
AU  - Mendes, S.
PY  - 2026
CY  - Guimarães
UR  - https://sites.google.com/view/wotca-2026
AB  - The study of $C^*$-algebras arising from number-theoretic data has its roots in the seminal construction of the Bost-Connes system, a landmark bridge between quantum statistical mechanics and the distribution of prime numbers. This program was later formalized and expanded by Cuntz, Li, Marcolli, Consani, Exel, among others, who developed a general framework to associate universal operator algebras with rings and integral domains through the representation of affine semigroups. 

In this talk, we investigate the $C^*$-algebraic structures associated with a specific category of commutative associative semifields. By relaxing the classical requirement for additive inverses, we uncover a novel class of algebras. We prove that these constructions naturally recover and generalize the classical Toeplitz algebra $\mathcal{T}$, identifying the ideal of compact operators as a fundamental geometric residue of the arithmetic space. Finally, we compute the $K$-theory of the associated $C^*$-algebras.
ER  -