15,179 research outputs found
G-algebras, twistings, and equivalences of graded categories
Given Z-graded rings A and B, we study when the categories gr-A and gr-B are
equivalent. We relate the Morita-type results of Ahn-Marki and del Rio to the
twisting systems introduced by Zhang. Using Z-algebras, we obtain a simple
proof of Zhang's main result. This makes the definition of a Zhang twist
extremely natural and extends Zhang's results.Comment: 13 pages; typos corrected and revised slightly; to appear in Algebras
and Representation Theor
Geometric idealizers
Let X be a projective variety, an automorphism of X, L a
-ample invertible sheaf on X, and Z a closed subscheme of X. Inside the
twisted homogeneous coordinate ring , let I be the right
ideal of sections vanishing at Z. We study the subring R = k + I of B. Under
mild conditions on Z and , R is the idealizer of I in B: the maximal
subring of B in which I is a two-sided ideal.
We give geometric conditions on Z and that determine the algebraic
properties of R, and show that if Z and are sufficiently general, in a
sense we make precise, then R is left and right noetherian, has finite left and
right cohomological dimension, is strongly right noetherian but not strongly
left noetherian, and satisfies right (where d = \codim Z) but fails
left . We also give an example of a right noetherian ring with infinite
right cohomological dimension, partially answering a question of Stafford and
Van den Bergh. This generalizes results of Rogalski in the case that Z is a
point in .Comment: 43 pages; comments welcom
Classifying birationally commutative projective surfaces
Let R be a noetherian connected graded domain of Gelfand-Kirillov dimension 3
over an uncountable algebraically closed field. Suppose that the graded
quotient ring of R is a skew-Laurent ring over a field; we say that R is a
birationally commutative projective surface. We classify birationally
commutative projective surfaces and show that they fall into four families,
parameterized by geometric data. This generalizes work of Rogalski and Stafford
on birationally commutative projective surfaces generated in degree 1; our
proof techniques are quite different.Comment: 60 pages; Proceedings of the LMS, 201
Implications of finite one-loop corrections for seesaw neutrino masses
In the standard seesaw model, finite corrections to the neutrino mass matrix
arise from one-loop self-energy diagrams mediated by a heavy neutrino. We
discuss the impact that these corrections may have on the different low-energy
neutrino observables paying special attention to their dependence with the
seesaw model parameters. It is shown that sizable deviations from the
tri-bimaximal mixing pattern can be obtained when these corrections are taken
into account.Comment: 4 pages, 3 figures. Prepared for the proceedings of the 12th
International Conference on Topics in Astroparticle and Underground Physics
(TAUP 2011), Munich, Germany, 5-9 September 201
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