Paul Smith's Papers

1.
The primitive factor rings of the enveloping algebra of
sl(2,C),
* J. London Math. Soc., * ** 24 ** (1981), no. 1, 97-108.
2.
The Krull dimension of the enveloping algebra of sl(2,C),
* J. Algebra, * ** 71 **
(1981) 189-194.
3.
An example of a ring Morita equivalent to the Weyl algebra
A_{1},
* J. Algebra, * ** 73 ** (1981) 552-555.
4.
Krull dimension of factor rings of the enveloping algebra of a
semisimple Lie algebra,
* Math. Proc. Cambridge Philos. Soc., * ** 93 **
(1983) 459-466.
5.
Central localization and Gelfand-Kirillov dimension,
* Israel J. Math., * ** 46** (1983) 33-39.
6.
Gelfand-Kirillov dimension of rings of formal differential
operators on affine varieties,
* Proc. Amer. Math. Soc., * **
90 ** (1984) 1-8.
7.
Sheaves of noncommutative algebras and the Beilinson-Bernstein
equivalence of categories (with T.J. Hodges),
* Proc. Amer. Math. Soc., * ** 93 ** (1985) 379-386.
8.
On the global dimension of certain primitive factors of the
enveloping algebra of a semisimple Lie algebra
(with T.J. Hodges),
* J. London Math. Soc., *
** 32 ** (1985) 411-418.
9.
Differential Operators on the Flag Variety and the Conze embedding,
(with T.J. Hodges), unpublished manuscript, University of
Warwick preprint (1984).
10.
Bimodules over a solvable algebraic Lie algebra
(with K.A. Brown),
* Quart. J. Math., * Ser. (2) ** 36 ** (1985) 129-139.
11.
Differential operators on the affine and projective lines in
characteristic p>0,
* Sem. d'alg. P. Dubreil et M.-P. Malliavin,
*
(Paris 1985), 157-177,
L.N.Math, ** 1220**, Springer, Berlin, 1986.
12.
The global homological dimension of the ring of differential
operators on a nonsingular variety over a field of positive
characteristic,
* J. Algebra, * ** 107 ** (1987) 98-105.
13.
Differential operators on commutative algebras,
Ring Theory Conf.,
(Antwerp, 1985), 165-177, Lecture Notes in Math., 1197,
Springer, Berlin, 1986.
14.
Differential operators on an affine curve
(with J.T. Stafford),
* Proc. London Math. Soc., * **
56 ** (1988) 229-259.
15.
Primitive ideals and nilpotent orbits in type G2
(with T. Levasseur), * J. Algebra, * ** 114
** (1988) 81-105.
Corrigendum
16.
Differential operators on some singular surfaces
(with R. Hart),
* Bull. London Math. Soc., * ** 19 ** (1987) 145-148.
17.
The simple D-module associated to the intersection homology complex
for a class of plane curves,
* J. Pure Appl. Algebra, * ** 50 ** (1988)
287-294.
18.
Curves, differential operators and finite-dimensional
algebras,
Sem. P. Dubreil et M.-P. Malliavin (Paris,
1986), 158-176, Lect. Notes in Math., 1296, Springer, Berlin,
1987.
19.
The minimal nilpotent orbit, the Joseph ideal, and differential
operators (with T. Levasseur and J,T. Stafford),
* J. Algebra, * ** 116 ** (1988) 480-501.
20.
A class of algebras similar to the enveloping algebra of sl(2),
* Trans. Amer. Math. Soc.i, * ** 322 ** (1990) 285-314.
21.
Overrings of primitive factor rings of U(sl(2,C)),
* J. Pure Appl.
Algebra, * ** 63 ** (1990) 207-218.
22.
Can the Weyl algebra be a fixed ring?
* Proc. Amer. Math. Soc., * ** 107 **
(1989) 587-589.
23.
Polynomial solutions to constant coefficient differential
equations,
* Trans. Amer. Math. Soc., * ** 329 ** (1992) 551-569.
24.
Skew derivations and Uq(sl(2)) (with S. Montgomery).
* Israel J. Math.,
* ** 72
**
(1990) 158-166.
25. +
Introduction to quantum groups for ring theorists,
* Proceedings of
1989 MSRI Conference on Non-commutative Noetherian Rings,* Ed. L.W.
Small, 1991, pp. 131-178.
26.
Regularity of the 4-dimensional Sklyanin algebra (with J.T.
Stafford),
* Compos. Math., * ** 83 ** (1992) 259-289.
27.
Modules over the 4-dimensional Sklyanin algebra
(with T. Levasseur),
* Bull. Soc. Math. France, * **121** (1993) 35-90.
28.
Irreducible representations of
4-dimensional Sklyanin algebras at points of infinite order
(with J. Staniszkis),
* J. Algebra,* ** 160 ** (1993) 57-86
29.
Homogenized sl(2)
(with L. Le Bruyn),
* Proc. Amer. Math. Soc.,* ** 118 ** (1993) 725-730.
30.
Central extensions of 3-dimensional
Artin-Schelter regular algebras
(with L. LeBruyn and M. van den Bergh),
*Math. Zeit.,* ** 222 ** (1996) 171-212.
31.+
The 4-dimensional Sklyanin algebra at points of finite order,
privately circulated manuscript
32.
Point modules over Sklyanin algebras,
* Math. Zeit.,* ** 215 ** (1994) 169-177.
33.
The 4-dimensional Sklyanin algebras,
Proc. of Conf. on Algebraic Geometry and Ring Theory in
honor of Michael Artin (Antwerp, 1992).
* K-Theory,* ** 8** (1994) 65-80.
34.
The center of the 3-dimensional and
4-dimensional Sklyanin algebras (with J. Tate),
* K-Theory, * ** 8 ** (1994) 19-63.
35.
Some finite dimensional algebras related to
elliptic curves,
Repn. theory of algebras (Mexico City,
1994), 315-348, CMS Conf. Proc., 19, Amer. Math. Soc.,
Providence, RI, 1996.
36.
Auslander-Gorenstein rings (with K. Ajitabh, and J.J. Zhang),
* Comm. Algebra,* ** 26** (1998) 2159-2180.
The preprint.
37.
Injective resolutions of some regular rings
(with K. Ajitabh, and J.J. Zhang),
* J. Pure Appl. Algebra, * ** 140 ** (1999) 1-21.
38.
Self-injective connected algebras (with J.J. Zhang),
* Comm. Alg., * ** 25 ** (1997) 2243-2248.
39.
A remark on Gelfand-Kirillov dimension
(with J.J. Zhang),
* Proc. Amer. Math. Soc., * ** 126**
(1998) 349-352.
40.
Curves on quasi-schemes (with J.J. Zhang),
* Algebr. Represent. Theory, * ** 1** (1998) 311-351.
41.
Bezout's Theorem for quantum projective spaces (with I. Mori),
* J. Pure Appl. Algebra, * ** 157 ** (2001) 279-299.
42.
The Grothendieck group of a quantum projective space bundle (with
I. Mori),
* K-Theory,* ** 37** (2006) 263-289.
43.
Fibers in Ore extensions (with J.J. Zhang),
*Algebr. Represent. Theory, * **5** (2002) 411-431.
44. +
Recognizing modules over dedekind domains, (with J.J. Zhang)
dvi
or ps
45.
Subspaces of Non-commutative Spaces,
* Trans. Amer. Math. Soc.,* ** 354** (2002) 2131-2171.
46.
Integral non-commutative spaces,
* J. Algebra, * ** 246 ** (2001) 793-810.
47.
Maps between non-commutative spaces,
* Trans. Amer. Math. Soc., * ** 356 ** (2004) 2927-2944.
48.
Representations of symplectic reflection algebras and resolutions of
deformations of symplectic quotient singularities (with
I. Gordon),
* Math. Ann.,* ** 330** (2004) 185-200.
49.
Computation of the Grothendieck and Picard groups of a complete
toric DM stack **X**
by using a homogeneous coordinate ring for **X**,
* Glasgow Math. Jour.,* ** 53** (2010) 97-113.
50.
A quotient stack related to the Weyl algebra,
* Journal of Algebra,* ** 345 ** (2011) 1-48.
51.
A generalization of Watt's Theorem: Right exact functors on module
categories (with Adam Nyman)
0806.0832
52.
A derived equivalence for a Del Pezzo surface of degree 6 over an
arbitrary field,
(with Mark Blunk and Sue Sierra)
* Journal of K-theory: K-theory and its Applications to Algebra,
Geometry, and Topology,* ** 8 ** (2011) 481-492.
arXiv:0908.3281
53.
A non-commutative homogeneous coordinate ring for the degree six
del Pezzo surface, * Journal of Algebra*,
** 354 ** (2012) 95-109.
54.
Noncommutative quadric surfaces
(with M. Van den Bergh),
* Journal of Noncommutative
Geometry,*
** 7 ** (2013) 817-856.
arXiv:1108.1552
55.
The space of Penrose tilings and the non-commutative curve with
homogeneous coordinate ring k{x,y}/(y^2),
*Journal of Noncommutative Geometry, accepted.*
arXiv:1104.3811
56.
The non-commutative scheme having a free algebra as a homogeneous
coordinate ring,
submitted to * Journal of Algebra*.
arXiv:1104.3822
57.
A 3-Calabi-Yau algebra with G_2 symmetry constructed from the
octonions,
arXiv:1104.3824
58.
Category equivalences involving graded modules over path algebras
of quivers,
*Advances in Mathematics,* **230** (2012) 1780-1810.
arXiv:1107.3511
59.
Shift equivalence and a category equivalence involving graded
modules over path algebras of quivers,
arXiv:1108.4994
60.
An equivalence of categories for graded modules over monomial
algebras and path algebras of quivers,
(with C. Holdaway)
* J. Algebra*, ** 353 ** (2012) 249-260.
arXiv:1109.4387
60b.
Corrigendum to
"An equivalence of categories for graded modules over monomial
algebras and path algebras of quivers",
(with C. Holdaway)
* J. Algebra*, ** 357 ** (2012) 319-321.
61.
Degenerate 3-dimensional Sklyanin algebras are monomial
algebras,
* Journal of Algebra*, ** 358 ** (2012) 74-86.
62.
Noncommutative complex differential geometry, (with E.J. Beggs)
* J. Geom. and Phys.,* (2013) 7-33.
arXiv:1209.3595v2
63.
Free subalgebras of the skew polynomial rings k[x,y][t;\sigma] and
k[x,x^{-1},y,y^{-1}][t;\sigma] ,
arXiv:1308.1694
64.
Free algebras arising from positive entropy automorphisms of
surfaces
,
arXiv:1308.3902
65.
Regular algebras of global dimension two, (with Gautam
Sisodia)
arXiv:1403.0640
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about noncommutative geometry and algebra.