The Leavitt path algebra of a graph
For any row-finite graph E and any field K we construct the Leavitt path algebra L ( E ) having coefficients in K. When K is the field of complex numbers, then L ( E ) is the algebraic analog of the Cuntz–Krieger algebra C ∗ ( E ) described in [I. Raeburn, Graph algebras, in: CBMS Reg. Conf. Ser. Ma...
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Published in | Journal of algebra Vol. 293; no. 2; pp. 319 - 334 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
15.11.2005
|
Subjects | |
Online Access | Get full text |
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Summary: | For any row-finite graph
E and any field
K we construct the
Leavitt path algebra
L
(
E
)
having coefficients in
K. When
K is the field of complex numbers, then
L
(
E
)
is the algebraic analog of the Cuntz–Krieger algebra
C
∗
(
E
)
described in [I. Raeburn, Graph algebras, in: CBMS Reg. Conf. Ser. Math., vol. 103, Amer. Math. Soc., 2005]. The matrix rings
M
n
(
K
)
and the Leavitt algebras
L
(
1
,
n
)
appear as algebras of the form
L
(
E
)
for various graphs
E. In our main result, we give necessary and sufficient conditions on
E which imply that
L
(
E
)
is simple. |
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ISSN: | 0021-8693 1090-266X |
DOI: | 10.1016/j.jalgebra.2005.07.028 |