The Latin-American conference on algebra, the XV Coloquio Latinoamericano de Algebra (Cocoyoc, Mexico), consisted of plenary sessions of general interest and special sessions on algebraic combinatorics, associative rings, cohomology of rings and algebras, commutative algebra, group representations, Hopf algebras, number theory, quantum groups, and representation theory of algebras. This proceedings volume contains original research papers related to talks at the colloquium. In addition, there are several surveys presenting important topics to a broad mathematical audience. There are also two invited papers by Raymundo Bautista and Roberto Martinez, founders of the Mexican school of representation theory of algebras. The book is suitable for graduate students and researchers interested in algebra.
Recent results on ring constructions for error-correcting codes by R. Alfaro and A. Kelarev Algebras determined by their left and right parts by I. Assem, F. U. Coelho, M. Lanzilotta, D. Smith, and S. Trepode The work of Roberto Martinez-Villa by E. L. Green A survey on fat points on a smooth quadric by E. Guardo Bautista and the development of the representation theory of Artin algebras by C. M. Ringel A survey on Nichols algebras by M. Takeuchi Approximations by modules of G-dimension zero by Y. Yoshino Representations of matched pairs of groupoids and applications to weak Hopf algebras by M. Aguiar and N. Andruskiewitsch On symmetries of quasicrystals by V. A. Artamonov Frattini-type and Fitting-type subgroups by M. J. Asiain Representations of the quantum algebra su$ q(1,1)$ and duality of $q$-orthogonal polynomials by N. M. Atakishiyev and A. U. Klimyk Internal bialgebroids, entwining structures and corings by G. Bohm The $A 2$ Ocneanu quantum groupoid by R. Coquereaux Skew Armendariz rings and annihilator ideals of skew polynomial rings by W. Cortes Quantum symmetric algebras as braided Hopf algebras by D. Flores de Chela Blowup algebras of ideals of vertex covers of bipartite graphs by I. Gitler, E. Reyes, and R. H. Villarreal Minimal elements in the poset of tilting modules by D. Happel and L. Unger Dynamical twists and quantization by E. Karolinsky, A. Stolin, and V. Tarasov On the combinatorial rank of Hopf algebras by V. K. Kharchenko and A. Andrade A tensor product of projective $G$-groups by I. Lizasoain The minimum degree of a surface that passes through all the points of a 0-dimensional scheme but a point P by L. Marino Primitive ideals and Jacobson radicals in Hopf Galois extensions by S. Montgomery On the algebraic decomposition of a centralizer algebra of the hyperoctahedral group by R. C. Orellana Quantum group global symmetries of quantum chains. States for linear chains with left end open and right end closed by S. Rodriguez-Romo One-sided Hopf algebras by S. Rodriguez-Romo and E. J. Taft BTZ black hole and Jacobi inversion for fundamental domains of infinite volume by F. L. Williams Galois correspondence theorem for Hopf algebra actions by T. Yanai On two-point differentiation and its generalization by A. G. Zavadskij.