1,879 research outputs found
On stated -skein modules
We mainly focus on Classical limit, Splitting map, and Frobenius homomorphism
for stated -skein modules, and Unicity Theorem for stated -skein
algebras.
Let be a marked three manifold. We use to denote the
stated -skein module of where is a nonzero complex number.
We build a surjective algebra homomorphism from to the coordinate
ring of some algebraic set, and prove it's Kernal consists of all nilpotents.
We prove the universal representation algebra of is isomorphic to
when has only one component and is connected. Furthermore
we show is isomorphic to , where
, is connected, and is obtained from by adding
one extra marking. We also prove the splitting map is injective for any marked
three manifold when , and show that the splitting map is injective (for
general ) if there exists at least one component of such that this
component and the boundary of the splitting disk belong to the same component
of .
We also establish the Frobenius homomorphism for , which is map from
to when is a primitive -th root of unity with
being coprime with and every component of contains at least one
marking. We also show the commutativity between Frobenius homomorphism and
splitting map. When is the thickening of an essentially bordered pb
surface, we prove the Frobenius homomorphism is injective and it's image lives
in the center. We prove the stated -skein algebra is
affine almost Azumaya when is an essentially bordered pb surface and
is a primitive -th root of unity with being coprime with , which
implies the Unicity Theorem for .Comment: 66 page
Determinants of the Withdrawal of Foreign-invested Enterprises: Evidence from China
Based on the industry and commerce annual report data, the present study uses the continuous-time nonparametric, parametric, and semi-parametric estimation to investigate the determinants influencing the withdrawal behaviour of foreign-invested enterprises. Through the survival analysis of 3,858 foreign-invested enterprises located in China from 2013 to 2020, the study found that operation profit, enterprise size and enterprise age have significantly negative impacts on the probability of enterprise withdrawal. At the industry-level and region-level, the improvement of industry entry rate and regional business environment ranking can significantly increase the probability of enterprise survival. The rise of the regional GDP growth rate and wage rate can significantly increase the probability of enterprise withdrawal. The study also found that the influence of some variables on enterprise withdrawal varies with different withdrawal patterns. After applying multiple models for estimation, similar results were replicated, which reinforced the validity of the conclusions offered in the present study
Finiteness and dimension of stated skein modules over Frobenius
When the quantum parameter is a root of unity of odd order. The
stated skein module has an
-module structure, where is a marked
three manifold. We prove is a finitely generated
-module when is compact, which furthermore indicates
the reduced stated skein module for the compact marked three manifold is finite
dimensional. We also give an upper bound for the dimension of
over when is compact.
For a pb surface , we use to denote the
image of the Frobenius map when is a root of unity of odd order .
Then lives in the center of the stated skein
algebra . Let be
the field of fractions of , and
be
. Then we show the dimension of
over
is where equals to the number of boundary
components of minus the Euler characteristic of .Comment: 31 page
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