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Generalizations of the Exterior Algebra.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Generalizations of the Exterior Algebra./
作者:	Lippold, Steven R.
面頁冊數:	1 online resource (123 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
Contained By:	Dissertations Abstracts International84-11B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30541044click for full text (PQDT)
ISBN:	9798379534158

Generalizations of the Exterior Algebra.
Lippold, Steven R.

Generalizations of the Exterior Algebra. - 1 online resource (123 pages)

Source: Dissertations Abstracts International, Volume: 84-11, Section: B.

Thesis (Ph.D.)--Bowling Green State University, 2023.

Includes bibliographical references

Staic first introduced the exterior GSC-operad ?S2Vd as a generalization of the exterior algebra in Staic (2020), which he used to give a linear map detS2:V2?6 → k with the property that detS2(?1?i<j?4(vi,j) = 0 if there exists 1 ? x < y < z ? 4 such that vx,y = vx,z = vy,z. In this dissertation, we start by further exploring ?S2V. We get results such as connections to graph theory, dimensions of ?S2V [n] as vector spaces, and a map detS2:V3?15 → k which generalizes the determinant map. Then, we give a further generalization of the exterior algebra first presented in Staic and Lippold (2022), denoted ?S3Vd. We discuss connections to hypergraphs, the dimensions of ?S3V2 [n] as vector spaces, and a map detS3:V2?20 → k which generalizes the determinant and the map detS2. Following this, we define maps detS3: Vd?(1/2)d(3d-1)(3d-2) → k for all d ? 2 with the property that detS3 (?1?i<j<k?3d(vi,j, k)) = 0 if there exists 1 ? x < y < z < t ? 3d such that v x,y,z = v x,y,t = vx,z,t=vy,z,t. Further, we show that detS3 is a SLd (k) invariant nontrivial linear map. Lastly, we further extend these constructions to discuss the graded vector space ?SrV.[Equations Omitted].

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379534158Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Edge partitionsIndex Terms--Genre/Form:

542853
Electronic books.

Generalizations of the Exterior Algebra.
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245 1 0 $a Generalizations of the Exterior Algebra.
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500 $a Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
500 $a Advisor: Staic, Mihai.
502 $a Thesis (Ph.D.)--Bowling Green State University, 2023.
504 $a Includes bibliographical references
520 $a Staic first introduced the exterior GSC-operad ?S2Vd as a generalization of the exterior algebra in Staic (2020), which he used to give a linear map detS2:V2?6 → k with the property that detS2(?1?i<j?4(vi,j) = 0 if there exists 1 ? x < y < z ? 4 such that vx,y = vx,z = vy,z. In this dissertation, we start by further exploring ?S2V. We get results such as connections to graph theory, dimensions of ?S2V [n] as vector spaces, and a map detS2:V3?15 → k which generalizes the determinant map. Then, we give a further generalization of the exterior algebra first presented in Staic and Lippold (2022), denoted ?S3Vd. We discuss connections to hypergraphs, the dimensions of ?S3V2 [n] as vector spaces, and a map detS3:V2?20 → k which generalizes the determinant and the map detS2. Following this, we define maps detS3: Vd?(1/2)d(3d-1)(3d-2) → k for all d ? 2 with the property that detS3 (?1?i<j<k?3d(vi,j, k)) = 0 if there exists 1 ? x < y < z < t ? 3d such that v x,y,z = v x,y,t = vx,z,t=vy,z,t. Further, we show that detS3 is a SLd (k) invariant nontrivial linear map. Lastly, we further extend these constructions to discuss the graded vector space ?SrV.[Equations Omitted].
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Edge partitions
653 $a Hyperedge partitions
653 $a Complete graph
653 $a Complete hypergraph
653 $a Exterior algebra
653 $a Determinant
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690 $a 0405
690 $a 0642
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a Bowling Green State University. $b Mathematics. $3 3429413
773 0 $t Dissertations Abstracts International $g 84-11B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30541044 $z click for full text (PQDT)