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Item type:Publication, Twisted tensor products of K3 with K3(Bellwether Publishing, Ltd., 2021-01-01)Jorge A. Guccione and Juan J. Guccione were supported by UBACyT 20020150100153BA (UBA) and PIP 11220110100800CO (CONICET). This work was supported by CONCYTEC-FONDECYT within the framework of the contest ?Proyectos de Investigaci?n B?sica 2020-01? [contract number 120-2020-FONDECYT]. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Solutions of the braid equation attached to power series(Taylor and Francis Ltd., 2024-01-01)Let K be an algebraically closed characteristic 0 field and let V be the K-vector space with basis (Formula presented.). In this paper we use the theory developed in [17] to associate with each power series (Formula presented.) satisfying (Formula presented.), an involutive solution (Formula presented.), of the braid equation, and we begin the study of this correspondence. For (Formula presented.), let Vn be the subspace of V generated by (Formula presented.). Each one of the solution s(f) induces by restriction a solution (Formula presented.) on (Formula presented.). We also begin the study of these solutions. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Set-theoretic type solutions of the braid equation(Academic Press Inc., 2024-04-15)In this paper we begin the study of set-theoretic type solution of the braid equation. Our theory includes set-theoretical solutions as basic examples. More precisely, the linear solution associated to a set-theoretic solution on a set X can be regarded as coming from the coalgebra kX, where k is a field and the elements of X are grouplike. We introduce and study a broader class of linear solutions associated in a similar way to more general coalgebras. We show that the relationships between set-theoretical solutions, q-cycle sets, q-braces, skew-braces, matched pairs of groups and invertible 1-cocycles remain valid in our setting. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, The lower side of the Newton polygon of hypothetical counterexamples to the plane Jacobian conjecture(Taylor and Francis Ltd., 2026-01-01)We prove that if the Jacobian conjecture in two variables is false and (P, Q) is a counterexample that is a standard (m, n)-pair, then the Newton polygon HH (P) of P must satisfy several restrictions that had not been found previously. This allows us to discard some of the corners found in [16, Remark 7.9] for HH (P), together with some of the infinite families found in [9, Theorem 2.25]. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Extensions of Linear Cycle Sets and Cohomology(Springer Science and Business Media Deutschland GmbH, 2023-03-01)We generalize the cohomology theory for linear cycle sets introduced by Lebed and Vendramin. Our cohomology classifies extensions of linear cycle sets by trivial ideals, whereas the cohomology of Lebed and Vendramin only deals with central ideals I (which are automatically trivial). Therefore our theory gives an analog to the theory of extensions of braces by trivial ideals constructed by Bachiller, but from a cohomological point of view. We also study the general notions of extensions of linear cycle sets and the equivalence of extensions. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Hopf Q -braces structures on rank one pointed Hopf algebras(World Scientific, 2025-01-01)In this paper we determine all the Hopf [Formula: see text]-brace structures on rank one pointed Hopf algebras and compute the socle of each one of them. We also identify which among them are Hopf skew-braces. Then we determine when two Hopf [Formula: see text]-brace structures on rank one pointed Hopf algebras are isomorphic, and, finally, we compute all the weak braiding operators on these Hopf algebras.1