3,710 research outputs found

    A Generalization of Martin's Axiom

    Get PDF
    We define the ℵ1.5\aleph_{1.5} chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom and implies certain uniform failures of club--guessing on ω1\omega_1 that don't seem to have been considered in the literature before.Comment: 36 page

    Leibniz Gauge Theories and Infinity Structures

    Get PDF
    We formulate gauge theories based on Leibniz(-Loday) algebras and uncover their underlying mathematical structure. Various special cases have been developed in the context of gauged supergravity and exceptional field theory. These are based on `tensor hierarchies', which describe towers of pp-form gauge fields transforming under non-abelian gauge symmetries and which have been constructed up to low levels. Here we define `infinity-enhanced Leibniz algebras' that guarantee the existence of consistent tensor hierarchies to arbitrary level. We contrast these algebras with strongly homotopy Lie algebras (L∞L_{\infty} algebras), which can be used to define topological field theories for which all curvatures vanish. Any infinity-enhanced Leibniz algebra carries an associated L∞L_{\infty} algebra, which we discuss.Comment: 50 pages, v2: refs added, new subsection 3.2, version to appear in Comm. Math. Phy
    • …
    corecore