# Luzius Grunenfelder

Telephone: (902) 494-3676

Office: 305

email: luzius@mathstat.dal.ca

## Current Research

Hopf algebras, deformations and
extensions.

Algebraic and geometric aspects
of multiparameter spectral theory.

Matrix algebras and matrix groups.
## Recent Publications

On Bimeasurings, (with M. Mastnak),
to appear in J. Pure Appl. Algebra.
Transitive action of Lie algebras,
(with M. Omladic, H. Radjavi), J. Pure Appl. Algebra 199 (2005), 87-93.
On semitransitive collections of
operators, (with J. Bernik, M. Mastnak, H. Radjavi, V.G. Troitsky), Semigroup
Forum 70 (2005), 463-450.
Cohomology of abelian matched pairs
and the Kac sequence, (with M. Mastnak), J. Algebra 276 (2004), 706-736.
About braided and ordinary Hopf
algebras, Milan j. math. 71 (2003), 121-140.
Maximal Jordan algebras of matrices
with bounded number of eigenvalues, (with T. Kosir, M. Omladic, H. Radjavi),
Israel J. of Math. 128 (2002), 53-75.
Semigroups generated by similarity
orbits, (with M. Omladic, H. Radjavi, A. Sourour), Semigroup Forum 62 (2001)
460-472.
Constructing pointed Hopf algebras
by Ore extensions, (with M. Beattie, S. Dascalescu), J. Algebra 225 (2000),
743-770.
Ascent and descent of finite
sequences of commuting endomorphisms, (with M. Omladic), Pacific J. Math. 191 (1999), 95-121.
On pointed Hopf algebras of
dimension p^n, (with M. Beattie, S. Dascalescu), Proc.
Amer. Math. Soc. 128 (2000), 361-367.
On the number of types of
finite dimensional Hopf algebras, (with M. Beattie, S. Dascalescu),
Invent. Math. 136 (1999), 1-7.
On groups generated by
elements of prime order, (with T. Kosir, M. Omladic, H. Radjavi),
Geom. Dedicata 75 (1999), 317-332.
Finiteness conditions, co-Frobenius
Hopf algebras and Quantum Groups, (with M. Beattie, S. Dascalescu, C. Nastasescu),
J. Algebra 200 (1998), 312-333.
Geometric aspects of Multiparameter
Spectral Theory, (with T. Kosir), Trans. Amer. Math. Soc. 350 (1998), 2525-2546.
Modules graded by G-sets, duality and
finiteness conditions, (with D. Bulacu, S. Dascalescu), J. Algebra 195 (1997),
624-633.
Koszul cohomology for finite families
of comodule maps and applications, (with T. Kosir), Comm. Algebra 25 (1997),
459-479.
Permutability of characters on algebras,
(with R. Guralnick, T. Kosir, H. Radjavi), Pacific J. Math. 178 (1997), 63-70.
On a representation of commuting maps by
tensor products, (with T. Kosir), Lin. Alg. Appl. 251 (1997), 215-222.
An algebraic approach to multiparameter
Spectral Theory, (with T. Kosir), Trans. Amer. Math. Soc. 348 (1996), 2983-2998.
Coalgebras and Spectral Theory in one and
several variables, (with T. Kosir), Oper. Th. Adv. and Appl. 87 (1996), 177-192.
## A selection of earlier publications

Algebraic aspects of control systems and
realizations, J. Algebra 165 (1994), 446-464.
Jordan analogs of the Burnside and
Jacobson transitivity theorems, (with M. Omladic, H. Radjavi), Pacific J. Math.
161 (1993), 335-346.
Linearly recursive sequences and operator
polynomials, (with M. Omladic), Lin. Alg. Appl. 182 (1993), 127-145.
Tangent cohomology, Hopf algebra actions
and deformations, J. Pure Appl. Algebra 65 (1990), 125-149.
(Co-)homology of commutative coalgebras,
Comm. Algebra 16 (1988), 514-576.
Families parametrized by coalgebras, (with
R. Pare), J. Algebra 107 (1987), 316-375.
Graded algebras and their Euler-Poincare series,
J. Pure Appl. Algebra 46 (1987), 165-178.
On a commutator theorem of Robert C. Thompson,
(with R. Pare, H. Radjavi), Lin. Multilin. Algebra 16 (1984), 129-131.
Clifford k-algebras and k*-groups, Math. Z.
185 (1984), 137-150.
Lower central series, augmentation quotients
and homology of groups, Comment. Math. Helv. 55 (1980), 159-177.
Isomorphic group rings woth non-isomorphic
coefficient rings, (with M. Parmenter), Can. Math. Bull. 23 (1980), 245-246.
On the homology of filtered and graded rings,
J. Pure Appl. Algebra 14 (1979), 21-37.
On the periodicity of the graded ring associated
with an integral group ring, (with F. Bachmann), J. Pure Appl. Algebra 5 (1974), 253-264.
Homological methods and the third dimension
subgroup, (with F. Bachmann), Comment. Math. Helv. 47 (1972), 526-531.
Ueber Lie-Ringe von Gruppen und ihre universellen
Enveloppen, (with F. Bachmann), Comment. Math. Helv. 47 (1972), 332-340.
Hopf-Algebren und Coradikal, Math. Z. 116 (1970),
166-182
## Scholarly Contributions

Book: Ueber die Struktur von Hopf-Algebren,
Juris Druck & Verlag, Zurich (1969).
Numerous refereeing jobs for
various research journals.
Assessing numerous dissertations.