bibkey: conrad2026exterior
authors: Keith Conrad
year: 2026
title: Exterior Powers
doi: null
url: https://kconrad.math.uconn.edu/blurbs/linmultialg/extmod.pdf
claim: "Exterior powers have alternating products and the ordered wedge basis; an exterior algebra on three generators has graded ranks 1, 3, 3, 1."
strata_touched: []
license: citation-only
triage: anchor

Exterior carriers and products

The author-hosted notes are undated in their text; the bibliographic year denotes the PDF version’s creation year in its metadata, not an asserted first-publication year. Theorem 4.2, p. 11, gives the ordered wedge basis and binomial rank. Theorem 10.2 and Example 10.3, p. 44, give the exterior algebra and the three-generator ranks. Example 8.9 and Theorem 8.10, p. 34, concern decomposability and its obstruction; the four-dimensional coordinate factorization used by the consumer is an explicit calculation there, not a quotation of Example 8.9.

These are classical intermediate inputs to the five-face projection, Definition 22.1, Theorem 22.2 and Assumption 22.4. The exterior product is not Boolean pointwise multiplication. Equal vector-space dimensions do not identify the products or provide a probability law or a physical field.