3,710 research outputs found
A Generalization of Martin's Axiom
We define the chain condition. The corresponding forcing axiom
is a generalization of Martin's Axiom and implies certain uniform failures of
club--guessing on that don't seem to have been considered in the
literature before.Comment: 36 page
Leibniz Gauge Theories and Infinity Structures
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 -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
( algebras), which can be used to define topological field theories
for which all curvatures vanish. Any infinity-enhanced Leibniz algebra carries
an associated algebra, which we discuss.Comment: 50 pages, v2: refs added, new subsection 3.2, version to appear in
Comm. Math. Phy
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