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Units and Leavitt Path Algebras

Pilewski, Nicholas J.
http://orcid.org/0000-0002-7142-8595
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1427464498

Abstract Details

2015, Doctor of Philosophy (PhD), Ohio University, Mathematics (Arts and Sciences).
An invertible algebra is defined to be an algebra with a basis consisting solely of units. Given a field K and a finite graph E, we give a condition on E equivalent to the Leavitt path algebra LK(E) being an invertible K-algebra, and consequently a condition equivalent to the Cohn path algebra CK(E) being an invertible K-algebra. Given a unital commutative ring R, sufficient conditions on E for the Leavitt path algebra LR(E) to be an invertible R-algebra are given. As a by-product, given a field K and a graph E with finitely many vertices, we completely identify in terms of E all those right LK(E)-modules B such that LK(E) is isomorphic to the direct sum of LK(E) and B as a right LK(E)-module. As another by-product, we show that given an arbitrary R-algebra A, matrix algebras over A and direct sums of these matrix algebras are invertible R-algebras. Additionally, we characterize the invertible semilocal algebras over a division ring, and consequently the invertible finite dimensional algebras over a division ring.
Sergio Lopez-Permouth, Ph.D. (Advisor)
E. Todd Eisworth, Ph.D. (Committee Member)
Dinh Van Huynh, Ph.D. (Committee Member)
Jeffrey Dill, Ph.D. (Committee Member)
79 p.
Mathematics
Leavitt path algebras; graph algebras; rings of matrices; units; linear independence

Recommended Citations

Citations

  • Pilewski, N. J. (2015). Units and Leavitt Path Algebras [Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1427464498

    APA Style (7th edition)

  • Pilewski, Nicholas. Units and Leavitt Path Algebras. 2015. Ohio University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1427464498.

    MLA Style (8th edition)

  • Pilewski, Nicholas. "Units and Leavitt Path Algebras." Doctoral dissertation, Ohio University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1427464498

    Chicago Manual of Style (17th edition)

ohiou1427464498
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This open access ETD is published by Ohio University and OhioLINK.