Translation operator for self-projective coalgebras, Comm. in Algebra Vol. 39 (11) (2011)
Galois coverings of pointed coalgebras, Journal of Algebra, 324 (11), 3169-3182 (2010).
Coxeter tranformation and inverses of Cartan matrices for coalgebras (with D. Simson), J. Algebra 324, No. 9, 2223-2248 (2010)
Special biserial coalgebras and representations of quantum SL(2) at a root of unity, J. Algebra (2012).
Representation theory of liftings of quantum planes (with L. Krop), J. Algebra and Applications vol. 8, no. 2 (2009) 259-287.
Quantized hyperalgebras of rank one (with L. Krop, Israel J. Math 2005)
pdf
We look at the rank one case, showing it has a smash product structure
u#U, whre u is the restricted analog. We explicitly describe prime
ideals, the center and block decompositon by means of the explicit action
of the ordinary enveloping algebra on the indecomposable projectives for
each block.
Spectra of quantized hyperalgebras (with L. Krop, Transactions AMS,
(2006) pdf
tex
-We describe the prime and primitive spectra of (Lusztig's) quantized hyperalgebras
(at roots of 1), obtaining a tensor product theorem for simple modules
and an analog of Duflo's Theorem. The results depend on crossed product
techniques.
A brief introduction to coalgebra representation theory to appear, in Hopf Algebras, DePaul Conf. Proc. pdf
Local theory almost split sequences for comodules (with M. Kleiner
and D Quinn.) Ferrara-Swansea Conf. Proc. 2006 pdf
-We construct sequences for finite-dimensional comodules that satisfy a
property somewhat weaker than being almost split. They are almost
split in cases predicted by our previous paper. When almost split
sequences exist, they are direct limits of almost split sequences over
finite-dimensional subcoalgebras.
Two-sided
ideals in some finite dimensional algebras
(with L. Krop and S. Catoiu) in: Proc. Conf. on Groups, Rings and
Lie and Hopf Algebras, Y. Bakhturin, ed. Kluwer 2002. pdf
Hereditary and path coalgebras (Comm. Alg 2002) dvi
pdf
-We show that pointed hereditary colagebras are precisely the path coalgebra
(of their Ext-quivers). This characterizes hereditary coalgebras
up to equivalence (k alg. closed)
Almost split sequences for comodules (with M. Kleiner and D. Quinn) -J. Alg. 2001 dvi
Linear cellular automata with boundary conditions (with B. Cortzen and J. Goldman) Lin. Alg. and Appl. 2000 ps dvi (diagrams missing)
Injective comodules for 2x2 quantum matrices (with L. Krop), Comm. Alg. 2000 dvi
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Hopf
Algebras, Proceeding of an International Conference at DePaul University,
Lecture Notes in Pure and Aplied Math.237, Marcel Dekker New York, 2004
(co-edited with J. Bergen and S. Catoiu) amazon.com
Groups,
Rings and Algebras, Proceedings of a Conference in honor of Donald Passman,
Madison, Wisconsin, June 2005. Contemp. Math, to appear.
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Other articles:
Risk formulae for
proportional betting (with M. Ingenoso)
-We give formulas for the probabiltiy of losing specified proportions of
one's bankroll for proportional Kelly betting. This is then related
to risk of ruin and games with constant return over standard deviation.
This allows for proportional Kelly betting in games such as poker.
Risk adjustment for
poker players (with M. Ingenoso)
- We provide fomulas for the excess pot odds needed to break even
in Certainty Equivalent at various fractional Kelly utility functions.
Expectation isn't Everything
- This article (originally appeared in the July 2005 twoplustwo.com magazine)
discusses bankroll requirements, the role of variance in game selection,
proportional betting and Kelly criterion for poker, and utility theory
for lonshot draws. Copies available on request.
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