Rationality of Parameterizing Varieties for Modules Over Finite-Dimensional Algebras
- Degree Grantor:
- University of California, Santa Barbara. Mathematics
- Degree Supervisor:
- Birge Huisgen-Zimmermann
- Place of Publication:
- [Santa Barbara, Calif.]
- Publisher:
- University of California, Santa Barbara
- Creation Date:
- 2014
- Issued Date:
- 2014
- Topics:
- Mathematics
- Keywords:
- Path algebras modulo relations,
Representation Theory,
Quivers, and
Algebra - Genres:
- Online resources and Dissertations, Academic
- Dissertation:
- M.A.--University of California, Santa Barbara, 2014
- Description:
One can use classical varieties to attack the problem of classifying finitely-generated modules over finite-dimensional algebras. Given such an algebra, one can write down a number of varieties which parameterize modules with certain isomorphism invariants. Furthermore, these varieties come with morphic actions by algebraic groups whose orbits are in one-to-one correspondence with isomorphism classes of such modules. Using path algebras modulo relations, we can exploit the quiver structure to learn about the structure of these varieties. We use this to give a proof of rationality of one such variety parameterizing graded modules.
- Physical Description:
- 1 online resource (53 pages)
- Format:
- Text
- Collection(s):
- UCSB electronic theses and dissertations
- Other Versions:
- http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:1584090
- ARK:
- ark:/48907/f3jw8c26
- ISBN:
- 9781321568547
- Catalog System Number:
- 990045118890203776
- Copyright:
- Nathan Saritzky, 2014
- Rights:
- In Copyright
- Copyright Holder:
- Nathan Saritzky
File | Description |
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Access: Public access | |
Saritzky_ucsb_0035N_12337.pdf | pdf (Portable Document Format) |