LEAVITT PATH ALGEBRAS OF FINITE GELFAND–KIRILLOV DIMENSION

By Adel Alahmadi, Hamed Alsulami, S. K. Jain, E. Zelmanov. 2012

81 citations recorded by the source corpus.

Groebner–Shirshov Basis and Gelfand–Kirillov dimension of the Leavitt path algebra are derived.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8315cc6259f41fe12e951d7a0c110851af974825

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In Algebra and Number Theory

1. P. Ara
2. Yuqun Chen
3. Kulumani M. Rangaswamy
4. Leonid A. Bokut
5. G. Abrams
6. Roozbeh Hazrat
7. M. Tomforde
8. Pavel S. Kolesnikov

In Geometry and Topology

1. P. Ara
2. Yuqun Chen
3. Kulumani M. Rangaswamy
4. Leonid A. Bokut
5. Pavel S. Kolesnikov

In Mathematical Physics

1. P. Ara
2. Kulumani M. Rangaswamy
3. Yuqun Chen
4. Leonid A. Bokut
5. G. Abrams
6. Roozbeh Hazrat
7. M. Tomforde
8. Aidan Sims

Citations in the corpus

• Finitely presented simple modules over Leavitt path algebras (2013, background): “From Theorem 5 of [6], it is interesting to observe that, for a finite graph E, the equivalent conditions of Theorem 1.”
• Gröbner–Shirshov bases and their calculation (2013, methodology): “(k, l)(i, j) = (i, j)(k, l) for k > l > i > j, (k, l)V[ j−1,1](i, j) = (i, j)(k, l)V[ j−1,1] for k > i > j > l, (t3, t2)(t2, t1) = (t2, t1)(t3, t1), (t3, t1)V[t2−1,1](t3, t2) = (t2, t1)(t3, t1)V[t2−1,1], (t, s)V[t2−1,1](t2, t1)W[t3−1,t1](t3, t1) = (t3, t2)(t, s)V[t2−1,1](t2, t1)W ′ [t3−1,t1], (t3, s”