1,918 research outputs found
Galois coverings of pointed coalgebras
We introduce the concept of a Galois covering of a pointed coalgebra. The
theory developed shows that Galois coverings of pointed coalgebras can be
concretely expressed by smash coproducts using the coaction of the automorphism
group of the covering. Thus the theory of Galois coverings is seen to be
equivalent to group gradings of coalgebras. An advantageous feature of the
coalgebra theory is that neither the grading group nor the quiver is assumed
finite in order to obtain a smash product coalgebra
Special biserial coalgebras and representations of quantum SL(2)
We develop the theory of special biserial and string coalgebras and other
concepts from the representation theory of quivers. These tools are then used
to describe the finite dimensional comodules and Auslander-Reiten quiver for
the coordinate Hopf algebra of quantum SL(2) at a root of unity. We also
describe the stable Green ring and compute quantum dimensions.Comment: previous section 2.2 removed, errors correcte
Coverings of graded pointed Hopf algebras
We introduce the concept of a covering of a graded pointed Hopf algebra. The
theory developed shows that coverings of a bosonized Nichols algebra can be
concretely expressed by biproducts using a quotient of the universal coalgebra
covering group of the Nichols algebra. If there are enough quadratic relations,
the universal coalgebra covering is given by the bosonization by the enveloping
group of the underlying rack.Comment: to appear in J. of Algebr
Coxeter transformation and inverses of Cartan matrices for coalgebras
Let C be a coalgebra and consider the Grothendieck groups of the categories
of the socle-finite injective right and left C-comodules. One of the main aims
of the paper is to study Coxeter transformation, and its dual, of a pointed
sharp Euler coalgebra C, and to relate the action of these transformations on a
class of indecomposable finitely cogenerated C-comodules N with almost split
sequences starting or ending with N. We also show that if C is a pointed
K-coalgebra such that the every vertex of the left Gabriel quiver of C has only
finitely many neighbours, then for any indecomposable non-projective left
C-comodule N of finite K-dimension, there exists a unique almost split sequence
of finitely cogenerated left C-comodules ending at N. We show that the
dimension vector of the Auslander-Reiten translate given by the Coxeter
transformation, if C is hereditary, or more generally, if inj.dim DN=1 and
Hom(C,DN)=0
Kelly fraction estimation for multiple correlated bets
It is well-known that expected portfolio growth is maximized by maximizing
expected logarithmic utility. This investment criterion is known as Kelly betting.
It has many optimality properties but is considered to be risky. Blackjack
teams and other advantage gamblers practice a fraction of the Kelly optimal to
decrease risk. Some hedge fund managers are thought to practice according to
Kelly principles. We use a continuous multivariate Geometric Brownian motion
model and present an interval estimate for the historical fraction for a portfolio
of correlated bets, possibly including a risk-free asset. Historical data comes
from a range of sources and the results provide a risk aversion statistic, which
corresponds to an isoelastic utility function and level of relative risk aversion
Domestic Counterinsurgency: How Counterinsurgency Tactics Combined With Laws Were Deployed Against Blacks Throughout U.S. History
Long before the United States engaged in counterinsurgency overseas in Iraq and Afghanistan, the United States engaged in counterinsurgency domestically against blacks. The history of America is a history of enduring conflict between black insurgents and white counterinsurgents. This conflict began centuries ago with the forced transport of enslaved blacks to America’s shores. From the beginning, whites employed all levers of national power including laws to suppress black resistance. The laws became counterinsurgency weapons launched against blacks in an internal conflict lasting generations
Domestic Counterinsurgency: How Counterinsurgency Tactics Combined With Laws Were Deployed Against Blacks Throughout U.S. History
Long before the United States engaged in counterinsurgency overseas in Iraq and Afghanistan, the United States engaged in counterinsurgency domestically against blacks. The history of America is a history of enduring conflict between black insurgents and white counterinsurgents. This conflict began centuries ago with the forced transport of enslaved blacks to America’s shores. From the beginning, whites employed all levers of national power including laws to suppress black resistance. The laws became counterinsurgency weapons launched against blacks in an internal conflict lasting generations
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