55,562 research outputs found
Cohomology of Heisenberg Lie Superalgebras
Suppose the ground field to be algebraically closed and of characteristic
different from and . All Heisenberg Lie superalgebras consist of two
super versions of the Heisenberg Lie algebras, and
with a nonnegative integer and a positive integer. The
space of a "classical" Heisenberg Lie superalgebra is the
direct sum of a superspace with a non-degenerate anti-supersymmetric even
bilinear form and a one-dimensional space of values of this form constituting
the even center. The other super analog of the Heisenberg Lie algebra,
, is constructed by means of a non-degenerate anti-supersymmetric
odd bilinear form with values in the one-dimensional odd center. In this paper,
we study the cohomology of and with
coefficients in the trivial module by using the Hochschild-Serre spectral
sequences relative to a suitable ideal. In characteristic zero case, for any
Heisenberg Lie superalgebra, we determine completely the Betti numbers and
associative superalgebra structure for their cohomology. In characteristic
case, we determine the associative superalgebra structures for the
divided power cohomology of and we also make an attempt to
determine the cohomology of by computing it in a
low-dimensional case.Comment: 19 page
Transmission area and two-photon correlated imaging
The relationship between transmission area of an object imaged and the
visibility of its image is investigated in a lensless system. We show that the
changes of the visibility are quite different when the transmission area is
varied by different manners. An increase of the transmission by adding the slit
number leads to a decrease of the visibility. While, the change is adverse when
the slit width is widened for a given distance between two slits.Comment: 10 pages, 4 figure
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