1,414 research outputs found
Chern-Weil theory for line bundles with the family Arakelov metric
We prove a result of Chern-Weil type for canonically metrized line bundles on
one-parameter families of smooth complex curves. Our result generalizes a
result due to J.I. Burgos Gil, J. Kramer and U. K\"uhn that deals with a line
bundle of Jacobi forms on the universal elliptic curve over the modular curve
with full level structure, equipped with the Petersson metric. Our main tool,
as in the work by Burgos Gil, Kramer and K\"uhn, is the notion of a b-divisor.Comment: 34 page
Finitely Presented Monoids and Algebras defined by Permutation Relations of Abelian Type, II
The class of finitely presented algebras A over a field K with a set of
generators x_{1},...,x_{n} and defined by homogeneous relations of the form
x_{i_1}x_{i_2}...x_{i_l}=x_{sigma(i_1)}x_{sigma(i_2)}...x_{sigma(i_l)}, where l
geq 2 is a given integer and sigma runs through a subgroup H of Sym_n, is
considered. It is shown that the underlying monoid S_{n,l}(H)=
<x_1,x_2,...,x_n|x_{i_1}x_{i_2}...x_{i_l}=x_{sigma(i_1)}x_{sigma(i_2)}...x_{\sigma
(i_l)}, sigma in H, i_1,...,i_l in {1,...,n}> is cancellative if and only if H
is semiregular and abelian. In this case S_{n,l}(H) is a submonoid of its
universal group G. If, furthermore, H is transitive then the periodic elements
T(G) of G form a finite abelian subgroup, G is periodic-by-cyclic and it is a
central localization of S_{n,l}(H), and the Jacobson radical of the algebra A
is determined by the Jacobson radical of the group algebra K[T(G)]. Finally, it
is shown that if H is an arbitrary group that is transitive then K[S_{n,l}(H)]
is a Noetherian PI-algebra of Gelfand-Kirillov dimension one; if furthermore H
is abelian then often K[G] is a principal ideal ring. In case H is not
transitive then K[S_{n,l}(H)] is of exponential growth.Comment: 8 page
Algebras and groups defined by permutation relations of alternating type
The class of finitely presented algebras over a field with a set of
generators and defined by homogeneous relations of the form
, where
runs through \Alt_{n}, the alternating group, is considered. The
associated group, defined by the same (group) presentation, is described. A
description of the radical of the algebra is found. It turns out that the
radical is a finitely generated ideal that is nilpotent and it is determined by
a congruence on the underlying monoid, defined by the same presentation
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