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Special Linear Group


Given a ring R with identity, the special linear group SL_n(R) is the group of n×n matrices with elements in R and determinant 1.

The special linear group SL_n(q), where q is a prime power, the set of n×n matrices with determinant +1 and entries in the finite field GF(q). SL_n(C) is the corresponding set of n×n complex matrices having determinant +1.

SL_n(q) is a subgroup of the general linear group GL_n(q) and is a Lie-type group. Both SL_n(R) and SL_n(C) are genuine Lie groups.


See also

General Linear Group, Special Orthogonal Group, Special Unitary Group

Portions of this entry contributed by David Terr

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References

Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. "The Groups GL_n(q), SL_n(q), PGL_n(q), and PSL_n(q)=L_n(q)." §2.1 in Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, p. x, 1985.

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Special Linear Group

Cite this as:

Terr, David and Weisstein, Eric W. "Special Linear Group." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpecialLinearGroup.html

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