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sl2C

SL2C, or Special Linear Group of degree 2 over the complex numbers, is a mathematical group that plays a significant role in various areas of mathematics and physics. It is defined as the group of 2x2 matrices with complex entries and determinant equal to 1. The group operation is matrix multiplication. SL2C is a non-abelian group, meaning that the order of multiplication matters.

The group SL2C has several important subgroups, including the Borel subgroup, which consists of upper triangular

SL2C is also closely related to the projective special linear group PSL2C, which is the quotient of

In physics, SL2C appears in the context of conformal field theory and string theory. It is the

SL2C is a rich and complex mathematical object, with many open problems and active areas of research.

matrices,
and
the
maximal
compact
subgroup,
which
consists
of
unitary
matrices.
These
subgroups
are
crucial
in
the
study
of
representations
of
SL2C.
SL2C
by
its
center.
PSL2C
is
a
simple
group,
meaning
it
has
no
non-trivial
normal
subgroups.
symmetry
group
of
the
complex
plane
under
Möbius
transformations,
which
are
fractional
linear
transformations.
These
transformations
are
important
in
the
study
of
black
holes
and
other
gravitational
phenomena.
Its
study
continues
to
be
an
important
area
of
inquiry
in
both
mathematics
and
physics.