683 research outputs found
Perverse coherent t-structures through torsion theories
Bezrukavnikov (later together with Arinkin) recovered the work of Deligne
defining perverse -structures for the derived category of coherent sheaves
on a projective variety. In this text we prove that these -structures can be
obtained through tilting torsion theories as in the work of Happel, Reiten and
Smal\o. This approach proves to be slightly more general as it allows us to
define, in the quasi-coherent setting, similar perverse -structures for
certain noncommutative projective planes.Comment: New revised version with important correction
Some algebraic properties of differential operators
First, we study the subskewfield of rational pseudodifferential operators
over a differential field K generated in the skewfield of pseudodifferential
operators over K by the subalgebra of all differential operators.
Second, we show that the Dieudonne' determinant of a matrix
pseudodifferential operator with coefficients in a differential subring A of K
lies in the integral closure of A in K, and we give an example of a 2x2 matrix
differential operator with coefficients in A whose Dieudonne' determiant does
not lie in A.Comment: 15 page
Cryptanalysis of group-based key agreement protocols using subgroup distance functions
We introduce a new approach for cryptanalysis of key agreement protocols
based on noncommutative groups. This approach uses functions that estimate the
distance of a group element to a given subgroup. We test it against the
Shpilrain-Ushakov protocol, which is based on Thompson's group F
Rational matrix pseudodifferential operators
The skewfield K(d) of rational pseudodifferential operators over a
differential field K is the skewfield of fractions of the algebra of
differential operators K[d]. In our previous paper we showed that any H from
K(d) has a minimal fractional decomposition H=AB^(-1), where A,B are elements
of K[d], B is non-zero, and any common right divisor of A and B is a non-zero
element of K. Moreover, any right fractional decomposition of H is obtained by
multiplying A and B on the right by the same non-zero element of K[d]. In the
present paper we study the ring M_n(K(d)) of nxn matrices over the skewfield
K(d). We show that similarly, any H from M_n(K(d)) has a minimal fractional
decomposition H=AB^(-1), where A,B are elements of M_n(K[d]), B is
non-degenerate, and any common right divisor of A and B is an invertible
element of the ring M_n(K[d]). Moreover, any right fractional decomposition of
H is obtained by multiplying A and B on the right by the same non-degenerate
element of M_n(K [d]). We give several equivalent definitions of the minimal
fractional decomposition. These results are applied to the study of maximal
isotropicity property, used in the theory of Dirac structures.Comment: 20 page
Symmetry analysis of crystalline spin textures in dipolar spinor condensates
We study periodic crystalline spin textures in spinor condensates with
dipolar interactions via a systematic symmetry analysis of the low-energy
effective theory. By considering symmetry operations which combine real and
spin space operations, we classify symmetry groups consistent with non-trivial
experimental and theoretical constraints. Minimizing the energy within each
symmetry class allows us to explore possible ground states.Comment: 19 pages, 4 figure
Affine configurations and pure braids
We show that the fundamental group of the space of ordered affine-equivalent
configurations of at least five points in the real plane is isomorphic to the
pure braid group modulo its centre. In the case of four points this fundamental
group is free with eleven generators.Comment: 5 pages, 1 figure, final version; to appear in Discrete &
Computational Geometry, available from the publishers at
http://www.springerlink.com/content/384516n7q24811ph
The braid groups of the projective plane and the Fadell-Neuwirth short exact sequence
International audienceWe study the pure braid groups of the real projective plane , and in particular the possible splitting of the Fadell-Neuwirth short exact sequence , where and , and is the homomorphism which corresponds geometrically to forgetting the last strings. This problem is equivalent to that of the existence of a section for the associated fibration of configuration spaces. Van Buskirk proved in 1966 that and admit a section if and . Our main result in this paper is to prove that there is no section if . As a corollary, it follows that and are the only values for which a section exists. As part of the proof, we derive a presentation of : this appears to be the first time that such a presentation has been given in the literature
Improvement of stabilizer based entanglement distillation protocols by encoding operators
This paper presents a method for enumerating all encoding operators in the
Clifford group for a given stabilizer. Furthermore, we classify encoding
operators into the equivalence classes such that EDPs (Entanglement
Distillation Protocol) constructed from encoding operators in the same
equivalence class have the same performance. By this classification, for a
given parameter, the number of candidates for good EDPs is significantly
reduced. As a result, we find the best EDP among EDPs constructed from [[4,2]]
stabilizer codes. This EDP has a better performance than previously known EDPs
over wide range of fidelity.Comment: 22 pages, 2 figures, In version 2, we enumerate all encoding
operators in the Clifford group, and fix the wrong classification of encoding
operators in version
Surgery groups of the fundamental groups of hyperplane arrangement complements
Using a recent result of Bartels and Lueck (arXiv:0901.0442) we deduce that
the Farrell-Jones Fibered Isomorphism conjecture in L-theory is true for any
group which contains a finite index strongly poly-free normal subgroup, in
particular, for the Artin full braid groups. As a consequence we explicitly
compute the surgery groups of the Artin pure braid groups. This is obtained as
a corollary to a computation of the surgery groups of a more general class of
groups, namely for the fundamental group of the complement of any fiber-type
hyperplane arrangement in the complex n-space.Comment: 11 pages, AMSLATEX file, revised following referee's comments and
suggestions, to appear in Archiv der Mathemati
- …