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