The group FQM-298 of the Junta de Andalucía, "Rings associated to Quantum models" is formed by 8 members and 4 collaborators. It has 5 active members. Among the members there are two University Professors and 3 Full Professor. The group currently has a total of 8 six-year periods of research. It includes specialists in the areas of Algebra and Geometry.

It is a very active group as can be seen from its production: 223 publications in journals, 165 contributions to congresses, participation in 165 R+D+i projects, and 73 teaching activities. They have participated as members of Master and final degree thesis committees and we have also participated in Phd committees.

The group encompasses several lines of research, all of which have the common denominator of Applications of algebraic and geometric techniques. Among these techniques are:

-K- Theory in regular rings.

-C*-algebras and Leavitt Path Algebras.

-Lie theory,

-Algebraic geometry.

-Holomorphic and modular curves

-Numerical semigroups and affine semigroups. Factorization

Each branch enjoys an active research in the areas mentioned above and as future work we always think about how we can work in the quantum environment.

The key words in our research are:

Steinberg algebra; graded ideal; self-similar graph algebra; Boolean dynamical system; graph algebra, weak cancellation, refinement monoid, nonstable K-theory, ideal lattice, Generalized Lie-type algebra, n-Lie algebra, n-Leibniz algebra, Superalgebra, Color algebra, Quasi-multiplicative basis, Structure theory, Graph, Module, Algebra, Structure theory, Drinfeld modular forms, Drinfeld modules,

Embedding dimensión, Frobenius number, genus, multiplicity, numerical semigroup, Non-unique factorization, numerical semigroup, factorization, length of a factorization, delta set, Divisor-closed submonoid, Archimedean component, Set of minimal distances, Non-unique factorizations, Commutative monoid, Cancellative monoid, Polyhedral cone, Finitely generated monoid.

APPLICATIONS OF ALGEBRO-GEOMETRIC TECHNIQUES: K-THEORY IN REGULAR RINGS, C * -ALGEBRAS AND LEAVITT PATH ALGEBRAS, THEORY OF LIE; ALGEBRAIC GEOMETRY, HOLOMORPHIC FOLIATIONS AND MODULAR CURVES.

FACTORIZATIONS IN NUMERICAL SEMIGROUPS AND AFFINE SEMIGROUPS.

Applications of algebraic and geometric techniques