614 research outputs found
The Problem of Differential Calculus on Quantum Groups
The bicovariant differential calculi on quantum groups of Woronowicz have the
drawback that their dimensions do not agree with that of the corresponding
classical calculus. In this paper we discuss the first-order differential
calculus which arises from a simple quantum Lie algebra. This calculus has the
correct dimension and is shown to be bicovariant and complete. But it does not
satisfy the Leibniz rule. For sl_n this approach leads to a differential
calculus which satisfies a simple generalization of the Leibniz rule.Comment: Contribution to the proceedings of the Colloquium on Quantum Groups
and Integrable Systems Prague, June 1996. amslatex, 9 pages. For related
information see http://www.mth.kcl.ac.uk/~delius/q-lie.htm
From Refuge to resistance: Botsabelo, Mafolofolo and Johannes Dinkwanyane: Missionaries and converts under the authority of the Zuid-Afrikaansche Republiek, 1860-1876
African Studies Seminar series. Paper presented 23 February, 1981In the 1870s the Transvaal witnessed an intensification
of struggles over land and labour. This development was
particularly marked in its eastern districts and was partly
stimulated by the impact on the local and regional political
economy of the discovery and exploitation of diamonds and
gold. Also important was the changing nature of Z.A.R.
control over, and intervention in, the countryside and the
growing power of the Pedi polity. The latter had by the
1870s emerged as an alternative focus of power and authority
to both the Z.A.R. and the Swazi kingdom. These factors
shaped the disputes which culminated in the war between the
Pedi and the Z.A.R. in 1876. This conflict in turn
provided one of the pretexts for the British annexation of
the Transvaal in early 1877
Sebatakgomo: Migrant organization, the ANC and the Sekhukhuneland Revolt
African Studies Seminar series. Paper presented. No dates given in the paper. No citations in copy. Marked 'Additional Seminar paper' and on the 1st page of text as 'informal'.In the 1940s and 1950s in reserve and trust area from the
Zoutpansberg to the Ciskei bitter battles were fought against
first Betterment Schemes and then Bantu Authorities. Communities
believed - with good reason - that these state initiatives posed a
mortal threat to their residual, but cherished, economic and
political autonomy. These episodes are usually treated under the
rubric of rural or peasant resistance but the centrality of
migrant labour to the South African political economy has always
undermined simple divisions between town and countryside. A
closer examination shows that in virtually every instance of
resistance urban-based migrant organizations played vital
roles. Yet this is difficult to explain for groups like the
Zoutpansberg Cultural Association, the Bahurutshe Association or
the Mpondo Association step almost entirely unheralded onto the
stage. We have the barest idea of the long history of
migrant organization which preceded their part in these events.
It has also become commonplace in the literature on 'rural
resistance' to suggest that the ANC, while not entirely
insensitive to rural issues in the 194Os and 1950s, nonetheless
failed to establish effective rural organization and played at
best a marginal role in the various revolts. This conclusion
is partly based on the sparseness of Congress branches in the
countryside. But it has been arrived at without any systematic
attempt to examine a crucial question. Did migrants and their
organizations provide a partly unseen but effective bridge
between the ANC, the SACP and rural politics?
These gaps in our understanding of 'rural resistance' will not
easily be filled . This article, however, attempts to provide
some illumination of these issues by means of a study of the role
of migrants in the Sekhukhuneland Revolt of 1957 — 1961. To give
some indication of the destination of the argument, the evidence
suggests that a movement established in 1954 from within the
ANC and the SACP - Sebatakqqmg - won widespread migrant
support and played a key role in organizing and sustaining the
resistance in the eastern Transvaal. The journey to this
conclusion will, however, be long and prone to detour - for in
order to be able to explain the interaction between migrants, the
ANC, and rural conflict in the 1950s it is necessary to trace
the changing patterns of Pedi employment and association from at
least the 1930s
Quantum Lie algebras associated to and
Quantum Lie algebras \qlie{g} are non-associative algebras which are
embedded into the quantized enveloping algebras of Drinfeld and Jimbo
in the same way as ordinary Lie algebras are embedded into their enveloping
algebras. The quantum Lie product on \qlie{g} is induced by the quantum
adjoint action of . We construct the quantum Lie algebras associated to
and . We determine the structure constants and the
quantum root systems, which are now functions of the quantum parameter .
They exhibit an interesting duality symmetry under .Comment: Latex 9 page
Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters
We present a systematic technique to construct solutions to the Yang-Baxter
equation which depend not only on a spectral parameter but in addition on
further continuous parameters. These extra parameters enter the Yang-Baxter
equation in a similar way to the spectral parameter but in a non-additive form.
We exploit the fact that quantum non-compact algebras such as
and type-I quantum superalgebras such as and are
known to admit non-trivial one-parameter families of infinite-dimensional and
finite dimensional irreps, respectively, even for generic . We develop a
technique for constructing the corresponding spectral-dependent R-matrices. As
examples we work out the the -matrices for the three quantum algebras
mentioned above in certain representations.Comment: 13 page
The structure of quantum Lie algebras for the classical series B_l, C_l and D_l
The structure constants of quantum Lie algebras depend on a quantum
deformation parameter q and they reduce to the classical structure constants of
a Lie algebra at . We explain the relationship between the structure
constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for
adjoint x adjoint ---> adjoint. We present a practical method for the
determination of these quantum Clebsch-Gordan coefficients and are thus able to
give explicit expressions for the structure constants of the quantum Lie
algebras associated to the classical Lie algebras B_l, C_l and D_l.
In the quantum case also the structure constants of the Cartan subalgebra are
non-zero and we observe that they are determined in terms of the simple quantum
roots. We introduce an invariant Killing form on the quantum Lie algebras and
find that it takes values which are simple q-deformations of the classical
ones.Comment: 25 pages, amslatex, eepic. Final version for publication in J. Phys.
A. Minor misprints in eqs. 5.11 and 5.12 correcte
Scanning Electron Microscopy of the Lateral Ventricle of the Pigeon Brain
Adult pigeons of both sexes were used for this study. Depending upon the distribution of various surface profiles, for example cilia, microvilli and blebs, ependymal areas with differing surface patterns were distinguished in the lateral ventricle. The topographical locations of these areas with respect to the underlying forebrain nuclei were determined in accord with the atlas of Karten and Hodos (1967). The medial surface (A) of the ventricle was much more densely ciliated than the lateral surface (B). There did not appear to be any correlation between a given surface pattern and a specific type of underlying nervous tissue. Comparison of the cell patterns seen in the pigeon brain with those seen in the analogous areas of the rat brain showed that it is not feasible to extrapolate from one zoological group to another.
With the exception of the Kolmer cells populating the choroid plexus, there were remarkably few supraependymal cells in the pigeon lateral ventricle. Supraependymal nerve fibers were also extremely rare. Particular attention was given to the ependyma associated with the nucleus stria terminalis, to that of the lateral septal organ and to the choroid plexus. The possible classification of these areas into the group of the circumventricular organs is considered
Reflection equation for the N=3 Cremmer-Gervais R-matrix
We consider the reflection equation of the N=3 Cremmer-Gervais R-matrix. The
reflection equation is shown to be equivalent to 38 equations which do not
depend on the parameter of the R-matrix, q. Solving those 38 equations. the
solution space is found to be the union of two types of spaces, each of which
is parametrized by the algebraic variety and .Comment: 28 pages, revised versio
Representations of the Generalized Lie Algebra sl(2)_q
We construct finite-dimensional irreducible representations of two quantum
algebras related to the generalized Lie algebra \ssll (2)_q introduced by
Lyubashenko and the second named author. We consider separately the cases of
generic and at roots of unity. Some of the representations have no
classical analog even for generic . Some of the representations have no
analog to the finite-dimensional representations of the quantised enveloping
algebra , while in those that do there are different matrix
elements.Comment: 14 pages, plain-TEX file using input files harvmac.tex, amssym.de
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