2,753 research outputs found
On Lie and associative algebras containing inner derivations
We describe subalgebras of the Lie algebra \mf{gl}(n^2) that contain all
inner derivations of (where and is an algebraically
closed field of characteristic 0). In a more general context where is a
prime algebra satisfying certain technical restrictions, we establish a density
theorem for the associative algebra generated by all inner derivations of .Comment: 11 pages, accepted for publication in Linear Algebra App
Lie Superautomorphisms on Associative Algebras, II
Lie superautomorphisms of prime associative superalgebras are considered. A
definitive result is obtained for central simple superalgebras: their Lie
superautomorphisms are of standard forms, except when the dimension of the
superalgebra in question is 2 or 4.Comment: 19 pages, accepted for publication in Algebr. Represent. Theor
Identifying derivations through the spectra of their values
We consider the relationship between derivations and of a Banach
algebra that satisfy \s(g(x)) \subseteq \s(d(x)) for every ,
where \s(\, . \,) stands for the spectrum. It turns out that in some basic
situations, say if , the only possibilities are that , , and,
if is an inner derivation implemented by an algebraic element of degree 2,
also . The conclusions in more complex classes of algebras are not so
simple, but are of a similar spirit. A rather definitive result is obtained for
von Neumann algebras. In general -algebras we have to make some
adjustments, in particular we restrict our attention to inner derivations
implemented by selfadjoint elements. We also consider a related condition
for all selfadjoint elements from a
-algebra , where and is normal.Comment: 12 page
Adjoint torelons, and the persistence of color electric flux tubes in the deconfined phase
It is argued that the adjoint torelon loop, i.e. a Polyakov loop in the
adjoint representation running in a spatial, rather than temporal, direction,
is an observable which is sensitive to the presence of long color electric flux
tubes at high temperatures. We show via lattice Monte Carlo simulations that
this observable has a sharp peak at the deconfinement transition, remains much
larger than the vacuum value for some range of , and falls below the
vacuum value for . This result suggests that long electric flux tubes
may persist for a finite range of temperatures past the deconfinement
transition, and at some stage disappear, presumably melting into a plasma of
gluons. As a side remark, we point out that our results at imply that
the eigenvalues of ordinary Polyakov loop holonomies in the confinement phase
have a slight tendency to attract rather than repel, which may be relevant to
certain models of confinement.Comment: 6 pages, 4 figure
Dimensional Reduction and the Yang-Mills Vacuum State in 2+1 Dimensions
We propose an approximation to the ground state of Yang-Mills theory,
quantized in temporal gauge and 2+1 dimensions, which satisfies the Yang-Mills
Schrodinger equation in both the free-field limit, and in a strong-field zero
mode limit. Our proposal contains a single parameter with dimensions of mass;
confinement via dimensional reduction is obtained if this parameter is
non-zero, and a non-zero value appears to be energetically preferred. A method
for numerical simulation of this vacuum state is developed. It is shown that if
the mass parameter is fixed from the known string tension in 2+1 dimensions,
the resulting mass gap deduced from the vacuum state agrees, to within a few
percent, with known results for the mass gap obtained by standard lattice Monte
Carlo methods.Comment: 14 pages, 9 figures. v2: Typos corrected. v3: added a new section
discussing alternative (new variables) approaches, and fixed a problem with
the appearance of figures in the pdf version. Version to appear in Phys Rev
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