vectors - 2026 ACF Regionals

Question

An algebra over a field consists of a “space” named for these objects that has a bilinear product. For 10 points each:

[10e] Name these objects have a magnitude and direction.

ANSWER: vectors [accept vector spaces]

[10m] This mathematician names a non-associative algebra that pairs a vector space with his namesake commutator bracket denoted “x y minus y x.” This mathematician names groups that are also differentiable manifolds.

ANSWER: Sophus Lie (“lee”) [or Marius Sophus Lie; accept Lie groups; accept Lie bracket; accept Lie algebra]

[10h] This adjective is prefixed by “semi” to describe Lie algebras that have a non-degenerate Killing form. Lie algebras described by this adjective are non-abelian (“non-uh-BEE-lee-un”) and contain no non-zero proper ideals.

ANSWER: simple [accept simple Lie algebras; accept semisimple Lie algebras]

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Summary


California (North)	Main Site	Y	3	26.67	100%	100%	67%
California (South)	Main Site	Y	4	17.50	100%	75%	0%
Canada	Main Site	Y	1	20.00	100%	100%	0%
Florida	Main Site	Y	3	13.33	100%	33%	0%
Great Lakes	Main Site	Y	5	14.00	100%	40%	0%
Lower Mid-Atlantic	Main Site	Y	8	12.50	100%	25%	0%
Midwest	Main Site	Y	8	15.00	100%	38%	13%
Northeast	Main Site	Y	5	16.00	100%	40%	20%
Overflow	Main Site	Y	3	10.00	100%	0%	0%
South Central	Main Site	Y	2	10.00	100%	0%	0%
Southeast	Main Site	Y	7	14.29	100%	29%	14%
UK	Main Site	Y	12	15.83	92%	50%	17%
Upper Mid-Atlantic	Main Site	Y	8	13.75	100%	38%	0%
Upstate NY	Main Site	Y	4	15.00	100%	25%	25%

Data


Stanford B	Berkeley B	10	10	0	20
Berkeley C	Stanford A	10	10	10	30
Berkeley A	Berkeley D	10	10	10	30
UC Irvine	UCLA B	10	10	0	20
UCSD C	UCLA A	10	10	0	20
UCSD A	UC Santa Barbara	10	0	0	10
UBC B	Brock	10	10	0	20
Florida C	Central Florida B	10	0	0	10
Central Florida A	Florida A	10	0	0	10
Central Florida C	Florida B	10	10	0	20
Michigan State	CWRU A	10	0	0	10
Ohio State A	Michigan A	10	10	0	20
Michigan B	Ohio State C	10	0	0	10
Michigan C	Pittsburgh	10	0	0	10
CWRU B	Ohio State B	10	10	0	20
James Madison B	William and Mary	10	0	0	10
James Madison A	Liberty A	10	0	0	10
Virginia Tech A	NC State A	10	10	0	20
NC State B	Liberty C	10	0	0	10
Liberty B	North Carolina C	10	0	0	10
South Carolina A	North Carolina B	10	0	0	10
VCU	Duke	10	10	0	20
Wake Forest	Virginia	10	0	0	10
Northwestern D	Chicago B	10	0	0	10
Chicago E	Chicago C	10	10	0	20
Notre Dame B	Illinois A	10	0	0	10
Illinois B	Indiana C	10	0	0	10
Illinois C	Purdue A	10	0	0	10
Indiana B	Purdue B	10	0	0	10
Northwestern B	Northwestern C	10	10	0	20
Indiana A	Notre Dame A	10	10	10	30
Bowdoin A	Yale	10	0	0	10
Brown	Harvard A	10	10	10	30
Dartmouth A	Dartmouth B	10	0	0	10
Harvard B	Bowdoin B	10	10	0	20
Brandeis A	Southern Connecticut State	10	0	0	10
Claremont	Minnesota A	10	0	0	10
Missouri B	Carleton College	10	0	0	10
Washington A	Iowa State	10	0	0	10
Texas A&M A	Murray State A	10	0	0	10
Texas B	Texas A	10	0	0	10
WashU B	Alabama A	10	0	0	10
Kentucky	WashU A	10	0	0	10
Georgia Tech B	Louisville A	10	0	0	10
Mississipi State	Georgia Tech D	10	0	0	10
Alabama B	Sewanee	10	0	0	10
Georgia Tech C	Tennessee A	10	10	10	30
Louisville B	Vanderbilt B	10	10	0	20
Arizona State	UCSD B	10	10	0	20
Birmingham	Montpellier	10	0	0	10
Bristol	Cambridge B	10	10	0	20
Cambridge A	Warwick A	10	10	0	20
City St. George's	Cambridge C	0	0	0	0
Southampton B	Cardiff	10	0	0	10
Edinburgh B	Durham	10	0	0	10
Oxford A	Imperial A	10	10	10	30
Southampton A	Imperial B	10	10	0	20
Oxford B	Imperial C	10	10	10	30
LSE	UCL	10	0	0	10
Manchester	Edinburgh A	10	10	0	20
Warwick B	Oxford C	10	0	0	10
Catholic	Johns Hopkins B	10	0	0	10
Columbia A	Maryland C	10	10	0	20
Columbia B	Maryland B	10	10	0	20
NYU C	John Jay	10	0	0	10
Cornell B	Binghamton B	10	0	10	20
Penn State	Cornell C	10	0	0	10
RIT	Cornell A	10	10	0	20
Binghamton A	Rochester	10	0	0	10
Maryland A	Rutgers A	10	10	0	20
Georgetown	Rutgers B	10	0	0	10
Columbia C	Swarthmore	10	0	0	10
NYU B	Vassar	10	0	0	10