Locally generalized projective lattices satisfying a bundle theorem

1987 ◽  
Vol 22 (3) ◽  
Author(s):  
LynnMargaret Batten
Keyword(s):  
Bundle Theorem ◽  
Projective Lattices

Relative characters for H-projective RG-lattices

1988 ◽  
Vol 104 (2) ◽  
pp. 207-213 ◽  
Author(s):  
Peter Symonds
Keyword(s):  
Representation Theory ◽  
Direct Summand ◽  
Modular Representation ◽  
Dedekind Domain ◽  
Modular Representation Theory ◽  
Trivial Group ◽  
Ordinary Character ◽  
Projective Lattices

If G is a group with a subgroup H and R is a Dedekind domain, then an H-projective RG-lattice is an RG-lattice that is a direct summand of an induced lattice for some RH-lattice N: they have been studied extensively in the context of modular representation theory. If H is the trivial group these are the projective lattices. We define a relative character χG/H on H-projective lattices, which in the case H = 1 is equivalent to the Hattori–Stallings trace for projective lattices (see [5, 8]), and in the case H = G is the ordinary character. These characters can be used to show that the R-ranks of certain H-projective lattices must be divisible by some specified number, generalizing some well-known results: cf. Corollary 3·6. If for example we take R = ℤ, then |G/H| divides the ℤ-rank of any H-projective ℤG-lattice.

The projective bundle theorem for Ij -cohomology

2013 ◽  
Vol 11 (2) ◽  
pp. 413-464 ◽  
Author(s):  
Jean Fasel
Keyword(s):  
Projective Bundle ◽  
Bundle Theorem

AbstractWe compute the total Ij -cohomology of a projective bundle over a smooth scheme.

Projective Geometries and Projective Lattices

2000 ◽  
pp. 25-53
Author(s):  
Claude-Alain Faure ◽  
Alfred Frölicher
Keyword(s):  
Projective Geometries ◽  
Projective Lattices

Distributive Projective Lattices

1970 ◽  
Vol 22 (3) ◽  
pp. 472-475 ◽  
Author(s):  
Kirby A. Baker ◽  
Alfred W. Hales
Keyword(s):  
Lattice Theory ◽  
Free Lattice ◽  
Important Case ◽  
Distributive Lattices ◽  
Interesting Corollary ◽  
Projective Lattices

Two basic unsolved problems of lattice theory are (1) the characterization of sublattices of free lattices and (2) the characterization of projective lattices. A solution to an important case of the first problem has been provided by Galvin and Jónsson [3], who characterize distributive sublattices of free lattices. In this paper, we solve the same case of the second problem by characterizing distributive projective lattices (Theorem 4.1). An interesting corollary is the verification for distributive lattices of the conjecture that a, finite lattice is projective if and only if it is a sublattice of a free lattice.

scholarly journals The special linear version of the projective bundle theorem

2014 ◽  
Vol 151 (3) ◽  
pp. 461-501 ◽  
Author(s):  
Alexey Ananyevskiy
Keyword(s):  
Polynomial Algebra ◽  
Characteristic Classes ◽  
Zero Section ◽  
Grassmann Variety ◽  
Special Linear ◽  
Bundle Theorem ◽  
Linear Version ◽  
Hopf Map ◽  
Ring Cohomology ◽  
Witt Groups

AbstractA special linear Grassmann variety $\text{SGr}(k,n)$ is the complement to the zero section of the determinant of the tautological vector bundle over $\text{Gr}(k,n)$. For an $SL$-oriented representable ring cohomology theory $A^{\ast }(-)$ with invertible stable Hopf map ${\it\eta}$, including Witt groups and $\text{MSL}_{{\it\eta}}^{\ast ,\ast }$, we have $A^{\ast }(\text{SGr}(2,2n+1))\cong A^{\ast }(pt)[e]/(e^{2n})$, and $A^{\ast }(\text{SGr}(k,n))$ is a truncated polynomial algebra over $A^{\ast }(pt)$ whenever $k(n-k)$ is even. A splitting principle for such theories is established. Using the computations for the special linear Grassmann varieties, we obtain a description of $A^{\ast }(\text{BSL}_{n})$ in terms of homogeneous power series in certain characteristic classes of tautological bundles.

A fiber bundle theorem

1992 ◽  
Vol 76 (1) ◽  
pp. 105-110 ◽  
Author(s):  
Helmut Reckziegel
Keyword(s):  
Fiber Bundle ◽  
Bundle Theorem
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