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ILLINOIS JOURNAL OF MATHEMATICS Volume 24, Number 2, Summer 1980
 

Summary: ILLINOIS JOURNAL OF MATHEMATICS
Volume 24, Number 2, Summer 1980
2-COHOMOLOGY OF SOME UNITARY GROUPS
BY
GEORGE S. AVRUNIN
In [1], we showed that the 2-cohomology of the group SU(n, q)with
coefficients in the standard module V l is generally zero. For SU(2, q),
which is, of course, equal to SL(2, q2), the only exceptions occur at q 2k
with
k _> 2; in unpublished work, McLaughlin has shown that the second cohom-
ology group has dimension 1 over Fq2. For n > 2 and q > 3, the only possible
exceptions are at n 3 with q 4 or 3k
and n 4 with q 4. In this paper, we
prove that H2(SU(n, q), V) has dimension 1 over Fq2 in the first case and
vanishes in the second. We also show that H2(SU(3, 3), V)is zero.
In Section l, we outline some basic results on the cohomology of groups. In
the second section, we compute HE(su(3, q), V) with q 4 or 3k, k > 1, while
the 2-cohomology of SU(4, 4) is determined in the third section. Finally, we
show H2(SU(3, 3), V)= 0 in the fourth section.
I. In this section, we describe some results on the cohomology of groups

  

Source: Avrunin, George S. - Department of Mathematics and Statistics, University of Massachusetts at Amherst

 

Collections: Mathematics